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%!PS-Adobe-2.0 %%Creator: dvips 5.58 Copyright 1986, 1994 Radical Eye Software %%Title: cocoon.dvi %%CreationDate: Sun Apr 25 19:16:08 1999 %%Pages: 18 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%EndComments %DVIPSCommandLine: %+ /afs/almaden.ibm.com/@sys/local/lib/texmf/bin/@sys/dvips558 %+ cocoon.dvi %DVIPSParameters: dpi=300, comments removed %DVIPSSource: TeX output 1999.04.25:1916 %%BeginProcSet: tex.pro /TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N /X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72 mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1} ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[matrix currentmatrix{dup dup round sub abs 0.00001 lt{round}if} forall round exch round exch]setmatrix}N /@landscape{/isls true N}B /@manualfeed{statusdict 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g(is)g(gro)o(wing)f(b)o(y)i(a)f(few)g(p)q(ercen)o(t)i(a)e(mon)o(th.)262 2412 y(The)i(a)o(v)o(erage)f(no)q(de)h(has)g(roughly)f(sev)o(en)h(h)o (yp)q(erlinks)g(\(directed)h(edges\))g(to)e(other)i(pages,)262 2462 y(making)c(for)i(a)h(total)f(of)h(sev)o(eral)g(billion)e(h)o(yp)q (erlinks)i(in)f(all.)p eop %%Page: 2 2 2 1 bop 324 224 a Fn(There)22 b(are)g(sev)o(eral)g(reasons)g(for)f (studying)g(the)h(W)m(eb)f(graph.)g(The)h(structure)h(of)262 274 y(this)15 b(graph)g(has)h(already)f(led)h(to)f(impro)o(v)o(ed)f(W)m (eb)h(searc)o(h)i([6,)5 b(8,)i(21,)f(29],)14 b(more)g(accurate)262 324 y(topic-classi\014cation)f(algorithms)g([11])g(and)h(has)g (inspired)h(algorithms)d(for)i(en)o(umerating)262 374 y(emergen)o(t)e(cyb)q(er-comm)o(unities)f([23].)g(The)i(h)o(yp)q (erlinks)g(themselv)o(es)g(represen)o(t)i(a)e(fecund)262 423 y(source)i(of)e(so)q(ciological)f(information.)e(Bey)o(ond)k(the)g (in)o(trinsic)g(in)o(terest)h(of)e(the)h(structure)262 473 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y(whic)o(h)f(W)m(eb)h(con)o(ten)o(t)g(is)g(created.)324 1019 y(In)f(Section)h(3)f(w)o(e)g(summarize)f(a)h(n)o(um)o(b)q(er)f(of) h(measuremen)o(ts)g(w)o(e)g(ha)o(v)o(e)h(made)e(on)h(the)262 1069 y(en)o(tire)f(W)m(eb)f(graph,)g(and)g(on)h(particular)f(lo)q(cal)g (subgraphs)h(of)f(in)o(terest.)i(W)m(e)e(sho)o(w,)g(for)g(in-)262 1119 y(stance,)i(that)f(the)h(in-)f(and)g(out-degrees)i(of)e(no)q(des)h (follo)o(w)d(Zip\014an)i(\(in)o(v)o(erse)i(p)q(olynomial)o(\))262 1169 y(distributions)j([12,)6 b(17,)g(26,)g(31].)16 b(This)h(and)h (other)g(measuremen)o(ts)g(of)f(the)h(frequency)h(of)262 1219 y(o)q(ccurrence)f(of)d(certain)i(structures)h(suggest)f(that)e (traditional)g(random)f(graph)i(mo)q(dels)262 1268 y(suc)o(h)e(as)g Ff(G)431 1274 y Fe(n;p)494 1268 y Fn([7])f(are)h(lik)o(ely)f(to)g(do)h (a)g(p)q(o)q(or)g(job)f(of)g(mo)q(deling)f(the)j(W)m(eb)e(graph.)324 1318 y(In)i(Section)h(4)f(w)o(e)g(la)o(y)g(do)o(wn)g(a)g(framew)o(ork)f (for)h(a)g(class)g(of)g(random)f(graph)h(mo)q(dels,)262 1368 y(and)j(giv)o(e)f(evidence)j(that)e(at)g(least)h(some)e(of)h(our)g (observ)n(ations)h(ab)q(out)f(the)h(W)m(eb)f(\(for)262 1418 y(instance,)12 b(the)g(degree)i(distributions\))d(can)i(b)q(e)f (established)h(in)e(these)i(mo)q(dels.)e(A)h(notable)262 1468 y(asp)q(ect)k(of)f(these)i(mo)q(dels)d(is)h(that)h(they)g(em)o(b)q (o)q(dy)e(some)h(v)o(ersion)g(of)g(a)g Fh(c)n(opying)h Fn(pro)q(cess:)262 1518 y(w)o(e)d(add)h(links)f(to)h(a)f(no)q(de)h Fd(v)i Fn(b)o(y)d(pic)o(king)g(a)g(random)g(\(other\))h(no)q(de)g Fd(u)g Fn(in)f(the)h(graph,)g(and)262 1567 y(cop)o(ying)f(some)h(links) f(from)g Fd(u)h Fn(to)g Fd(v)i Fn(\(i.e.,)d(w)o(e)h(add)h(edges)g(from) d Fd(v)k Fn(to)f(some)e(of)h(the)h(no)q(des)262 1617 y(that)e Fd(u)h Fn(p)q(oin)o(ts)g(to\).)f(Suc)o(h)i(cop)o(ying)e(op)q (erations)h(seem)g(to)g(b)q(e)g(fundamen)o(tal)e(b)q(oth)i(to)g(the)262 1667 y(pro)q(cess)i(of)f(con)o(ten)o(t-creation)g(on)g(the)h(W)m(eb)e (and)h(to)g(the)g(explanation)f(of)g(the)i(statistics)262 1717 y(w)o(e)f(ha)o(v)o(e)h(observ)o(ed.)g(One)h(consequence)h(is)d (that)h(the)h(mathematical)12 b(analysis)j(of)g(these)262 1767 y(graph)k(mo)q(dels)f(promises)h(to)g(b)q(e)h(far)g(harder)g(than) f(in)g(traditional)f(graph)i(mo)q(dels)e(in)262 1816 y(whic)o(h)13 b(the)i(edges)g(emanating)d(from)g(a)h(no)q(de)i(are)f (dra)o(wn)g(indep)q(enden)o(tly)m(.)324 1866 y(W)m(e)f(conclude)i(in)e (Section)i(5)e(with)h(a)f(n)o(um)o(b)q(er)h(of)f(directions)h(for)g (further)h(w)o(ork.)262 1986 y Fg(1.2)47 b(Related)14 b(w)o(ork)262 2064 y Fn(Analysis)d(of)g(the)i(structure)h(of)d(the)i(W) m(eb)f(graph)f(has)h(b)q(een)h(used)g(to)f(enhance)h(the)g(qualit)o(y) 262 2113 y(of)i(W)m(eb)h(searc)o(h)h([5,)6 b(6,)g(8,)g(9,)h(21,)f(29].) 14 b(The)j(topics)f(of)g(pages)g(p)q(oin)o(ted)h(to)f(b)o(y)g(a)g(W)m (eb)f(page)262 2163 y(can)d(b)q(e)i(used)f(to)g(impro)o(v)o(e)d(the)k (accuracy)f(of)f(determining)g(the)h(\(unkno)o(wn\))g(topic)f(of)g (this)262 2213 y(page)h(in)h(the)g(setting)h(of)e(sup)q(ervised)i (classi\014cation)f([11].)324 2263 y(Statistical)f(analysis)h(of)f(the) i(structure)h(of)e(the)g(academic)g(citation)f(graph)h(has)g(b)q(een) 262 2313 y(the)g(sub)r(ject)i(of)e(m)o(uc)o(h)f(w)o(ork)g(in)h(the)h (So)q(ciometrics)f(comm)o(unit)o(y)l(.)d(As)j(w)o(e)h(discuss)g(b)q (elo)o(w,)262 2363 y(Zipf)c(distributions)g(seem)h(to)f(c)o (haracterize)j(W)m(eb)d(citation)g(frequency)m(.)h(In)o(terestingly)m (,)f(the)262 2412 y(same)i(distributions)h(ha)o(v)o(e)h(also)e(b)q(een) j(observ)o(ed)f(for)f(citations)h(in)f(the)h(academic)e(litera-)262 2462 y(ture.)h(This)g(fact,)g(kno)o(wn)g(as)h Fh(L)n(otka's)g(law)p Fn(,)e(w)o(as)h(demonstrated)h(b)o(y)f(Lotk)n(a)f(in)h(1926)f([26].)p eop %%Page: 3 3 3 2 bop 262 224 a Fn(Gilb)q(ert)12 b([17])g(presen)o(ts)k(a)d (probabilistic)f(mo)q(del)g(explaining)g(Lotk)n(a's)g(la)o(w,)g(whic)o (h)h(is)g(sim-)262 274 y(ilar)j(in)h(spirit)g(to)h(our)f(prop)q(osal,)g (though)g(di\013eren)o(t)i(in)e(details)g(and)g(application.)f(The)262 324 y(\014eld)g(of)f(bibliometrics)f([14,)6 b(16])15 b(has)h(studied)h(phenomena)e(in)h(citation;)e(some)i(of)f(these)262 374 y(insigh)o(ts)e(ha)o(v)o(e)h(b)q(een)h(applied)e(to)h(the)g(W)m(eb) g(as)g(w)o(ell)f([25].)324 424 y(A)20 b(view)g(of)f(the)i(W)m(eb)e(as)h (a)g(semi-structured)h(database)f(has)g(b)q(een)i(adv)n(anced)e(b)o(y) 262 473 y(man)o(y)15 b(authors.)j(In)g(particular,)f(LORE)h([1])e(and)i (W)m(ebSQL)g([27])e(use)i(graph-theoretic)262 523 y(and)f(relational)g (views)i(of)e(the)i(W)m(eb)f(resp)q(ectiv)o(ely)m(.)g(These)i(views)e (supp)q(ort)h(structured)262 573 y(query)c(in)o(terfaces)i(to)e(the)h (W)m(eb)f(\(Lorel)g([1])f(and)h(W)m(ebSQL)h([27]\))d(that)j(are)g(ev)o (o)q(cativ)o(e)f(of)262 623 y(and)j(similar)f(to)h(SQL.)h(An)g(adv)n (an)o(tage)f(of)g(this)h(approac)o(h)g(is)g(that)g(man)o(y)e(in)o (teresting)262 673 y(queries)c(can)f(b)q(e)h(expressed)i(as)d(simple)f (expressions)i(in)f(the)h(v)o(ery)g(p)q(o)o(w)o(erful)e(SQL)i(syn)o (tax.)262 722 y(The)g(corresp)q(onding)g(disadv)n(an)o(tage)f(is)h (that)g(the)g(generalit)o(y)f(comes)h(with)f(an)h(asso)q(ciated)262 772 y(computational)f(cost)j(whic)o(h)g(can)g(b)q(e)g(prohibitiv)o(e)f (un)o(til)f(w)o(e)i(dev)o(elop)g(query)g(optimizers)262 822 y(for)f(W)m(eb)g(graph)h(computations)e(that)i(similar)e(to)h (those)i(a)o(v)n(ailable)c(for)j(relational)e(data.)262 872 y(LORE)f(and)h(W)m(ebSQL)g(are)h(but)f(t)o(w)o(o)f(examples)g(of)h (pro)r(jects)h(in)e(this)h(space.)h(Some)e(other)262 922 y(examples)g(are)h(W3QS)g([22],)e(W)m(ebQuery)j([8],)e(W)m(eblog)f ([24],)h(and)h(P)o(araSite/Squeal)f([29].)324 972 y(T)m(raditional)h (data)i(mining)e(researc)o(h)k(\(see)g(for)e(instance)h(Agra)o(w)o(al)e (and)h(Srik)n(an)o(t)g([2]\))262 1022 y(fo)q(cuses)f(largely)e(on)h (algorithms)e(for)i(\014nding)g(asso)q(ciation)g(rules)h(and)f(related) h(statistical)262 1071 y(correlation)j(measures)h(in)f(a)g(giv)o(en)h (dataset.)f(Ho)o(w)o(ev)o(er,)h(e\016cien)o(t)g(metho)q(ds)f(suc)o(h)i (as)e Fh(a)262 1121 y(priori)h Fn([2])c(or)i(ev)o(en)g(more)f(general)g (metho)q(dologies)f(suc)o(h)i(as)g Fh(query)h(\015o)n(cks)f Fn([30],)d(do)j(not)262 1171 y(scale)10 b(to)f(the)i(n)o(um)o(b)q(ers)e (of)g(\\items")g(\(pages\))h(in)f(the)i(W)m(eb)e(graph.)g(This)h(n)o (um)o(b)q(er)f(is)h(already)262 1221 y(t)o(w)o(o)16 b(to)h(three)h (orders)g(of)e(magnitude)f(more)h(than)h(the)g(n)o(um)o(b)q(er)f(of)g (items)g(in)h(a)f(t)o(ypical)262 1271 y(mark)o(et)c(bask)o(et)j (analysis.)324 1321 y(The)f(w)o(ork)g(of)g(Mendelzon)h(and)f(W)m(o)q(o) q(d)f([28])f(is)i(an)g(instance)h(of)f(structural)h(metho)q(ds)262 1370 y(in)f(mining.)d(They)k(argue)g(that)g(the)g(traditional)e(SQL)i (query)g(in)o(terface)g(to)f(databases)i(is)262 1420 y(inadequate)d(in)g(its)h(p)q(o)o(w)o(er)g(to)f(sp)q(ecify)h(sev)o (eral)g(structural)h(queries)f(that)g(are)g(in)o(teresting)262 1470 y(in)h(the)h(con)o(text)h(of)e(the)h(W)m(eb.)f(They)h(pro)o(vide)g (the)h(example)d(of)h(path)h(connectivit)o(y)g(b)q(e-)262 1520 y(t)o(w)o(een)g(no)q(des)h(sub)r(ject)g(to)e(some)g(constrain)o (ts)i(on)e(the)i(sequence)h(of)d(edges)i(on)e(the)h(path)262 1570 y(\(expressible)d(in)f(their)g(case)h(as)g(a)e(regular)i (expression\).)f(They)h(describ)q(e)h Fd(G)1460 1555 y Fm(+)1487 1570 y Fn(,)e(a)f(language)262 1620 y(with)i(greater)i (expressibilit)o(y)f(than)g(SQL)g(for)f(graph)h(queries.)262 1753 y Fi(2)56 b(Algorithms)262 1854 y Fn(W)m(e)19 b(ha)o(v)o(e)g (observ)o(ed)h(the)g(follo)o(wing)d(recurren)o(t)22 b(phenomenon)c(on)h (the)h(W)m(eb.)f(F)m(or)g(an)o(y)262 1904 y(particular)14 b(topic,)g(there)j(tend)e(to)g(b)q(e)g(a)g(set)g(of)g(\\authoritativ)o (e")e(pages)i(fo)q(cused)h(on)f(the)262 1954 y(topic,)10 b(and)h(a)g(set)h(of)e(\\h)o(ub")h(pages,)g(eac)o(h)h(con)o(taining)e (links)g(to)h(useful,)g(relev)n(an)o(t)g(pages)h(on)262 2004 y(the)i(topic.)e(This)i(observ)n(ation)f(motiv)n(ated)e(the)j(dev) o(elopmen)o(t)f(of)f(t)o(w)o(o)h(algorithms)f(whic)o(h)262 2053 y(w)o(e)g(describ)q(e)j(b)q(elo)o(w.)d(The)h(\014rst)h(is)e(a)h (searc)o(h)g(algorithm)d(that)j(distils)f(high-qualit)o(y)f(pages)262 2103 y(for)16 b(a)h(topic)g(query)g(\(Section)h(2.1\),)d(and)i(the)h (second)g(en)o(umerates)f(all)f(topics)h(that)g(are)262 2153 y(represen)o(ted)i(on)e(the)g(W)m(eb)f(in)h(terms)f(of)g(suitably) g(dense)j(sets)f(of)e(suc)o(h)h(h)o(ub/authorit)o(y)262 2203 y(pages)d(\(Section)g(2.2\).)262 2328 y Fg(2.1)47 b(The)16 b(HITS)g(algorithm)262 2412 y Fn(Beginning)11 b(with)g(a)g(searc)o(h)i(topic,)e(sp)q(eci\014ed)i(b)o(y)f(one)g(or)f (more)g(query)h(terms,)f(Klein)o(b)q(erg's)262 2462 y(HITS)j(algorithm) e([21])i(applies)g(t)o(w)o(o)g(main)f(steps:)j(a)e Fh(sampling)19 b Fn(step,)c(whic)o(h)f(constructs)p eop %%Page: 4 4 4 3 bop 262 224 a Fn(a)14 b(fo)q(cused)i(collection)e(of)g(sev)o(eral)i (thousand)f(W)m(eb)f(pages)h(lik)o(ely)f(to)h(b)q(e)g(ric)o(h)g(in)f (relev)n(an)o(t)262 274 y(authorities;)8 b(and)i(a)f Fh(weight-pr)n(op)n(agation)j Fn(step,)e(whic)o(h)f(determines)h(n)o (umerical)e(estimates)262 324 y(of)h(h)o(ub)h(and)g(authorit)o(y)g (scores)h(b)o(y)f(an)g(iterativ)o(e)g(pro)q(cedure.)i(The)e(pages)h (with)e(the)i(highest)262 374 y(scores)k(are)f(returned)i(as)e(h)o(ubs) g(and)g(authorities)g(for)f(the)i(searc)o(h)g(topic.)324 438 y(An)o(y)f(subset)i Fd(S)h Fn(of)d(no)q(des)i(induces)f(a)f Fh(sub)n(gr)n(aph)h Fn(con)o(taining)f(all)f(edges)j(that)e(connect)262 488 y(t)o(w)o(o)k(no)q(des)i(in)e Fd(S)r Fn(.)h(The)g(\014rst)h(step)g (of)e(the)i(HITS)e(algorithm)f(constructs)k(a)d(subgraph)262 537 y(exp)q(ected)f(to)f(b)q(e)h(ric)o(h)e(in)h(relev)n(an)o(t,)f (authoritativ)o(e)g(pages,)h(in)f(whic)o(h)h(it)f(will)g(searc)o(h)i (for)262 587 y(h)o(ubs)e(and)h(authorities.)e(T)m(o)h(construct)i(this) f(subgraph,)f(the)h(algorithm)d(\014rst)j(uses)h(k)o(ey-)262 637 y(w)o(ord)10 b(queries)i(to)e(collect)h(a)g Fh(r)n(o)n(ot)g(set)g Fn(of,)f(sa)o(y)m(,)f(200)h(pages)h(from)e(a)i(traditional)e (index-based)262 687 y(searc)o(h)18 b(engine.)f(This)g(set)h(do)q(es)g (not)f(necessarily)i(con)o(tain)d(authoritativ)o(e)h(pages;)g(ho)o(w-) 262 737 y(ev)o(er,)i(since)h(man)o(y)d(of)h(these)j(pages)e(are)g (presumably)f(relev)n(an)o(t)h(to)g(the)h(searc)o(h)g(topic,)262 787 y(one)13 b(can)g(exp)q(ect)i(some)d(to)h(con)o(tain)f(links)h(to)g (prominen)o(t)e(authorities,)i(and)g(others)h(to)f(b)q(e)262 836 y(link)o(ed)g(to)h(b)o(y)g(prominen)o(t)e(h)o(ubs.)i(The)h(ro)q(ot) f(set)h(is)f(therefore)h(expanded)g(in)o(to)f(a)f Fh(b)n(ase)j(set)262 886 y Fn(b)o(y)e(including)f(all)g(pages)i(that)f(are)h(link)o(ed)e(to) h(b)o(y)g(pages)h(in)f(the)h(ro)q(ot)f(set,)h(and)f(all)f(pages)262 936 y(that)g(link)f(to)h(a)g(page)g(in)g(the)h(ro)q(ot)f(set)h(\(up)g (to)f(a)g(designated)g(size)h(cut-o\013)s(\).)g(This)f(follo)o(ws)262 986 y(the)i(in)o(tuition)e(that)i(the)g(prominence)f(of)g(authoritativ) o(e)g(pages)h(is)g(t)o(ypically)e(due)i(to)g(the)262 1036 y(endorsemen)o(ts)d(of)e(man)o(y)g(relev)n(an)o(t)h(pages)h(that)f (are)h(not,)e(in)h(themselv)o(es,)g(prominen)o(t.)f(W)m(e)262 1085 y(restrict)18 b(our)f(atten)o(tion)f(to)h(this)g(base)g(set)h(for) e(the)i(remainder)e(of)g(the)i(algorithm;)13 b(this)262 1135 y(set)i(t)o(ypically)d(con)o(tains)i(roughly)g(1000{3000)d(pages,) j(and)g(that)g(\(hidden\))h(among)d(these)262 1185 y(are)k(a)g(large)g (n)o(um)o(b)q(er)f(of)g(pages)i(that)f(one)g(w)o(ould)f(sub)r(jectiv)o (ely)i(view)f(as)g(authoritativ)o(e)262 1235 y(for)d(the)i(searc)o(h)g (topic.)324 1299 y(W)m(e)i(b)q(egin)h(with)f(one)h(mo)q(di\014cation)d (to)j(the)g(subgraph)g(induced)g(b)o(y)g(the)g(base)g(set.)262 1349 y(Links)d(b)q(et)o(w)o(een)j(t)o(w)o(o)d(pages)i(on)f(the)h(same)e (W)m(eb)g(site)i(v)o(ery)f(often)h(serv)o(e)g(a)f(purely)g(na)o(v-)262 1399 y(igational)i(function,)i(and)g(t)o(ypically)g(do)g(not)h (represen)o(t)i(conferral)e(of)f(authorit)o(y)m(.)f(W)m(e)262 1449 y(therefore)e(delete)g(all)e(suc)o(h)i(links)e(from)f(the)j (subgraph)f(induced)h(b)o(y)f(the)g(base)h(set,)g(and)262 1498 y(apply)c(the)h(remainder)f(of)h(the)g(algorithm)d(to)j(this)g(mo) q(di\014ed)f(subgraph.)324 1563 y(Go)q(o)q(d)j(h)o(ubs)h(and)f (authorities)g(can)h(b)q(e)g(extracted)h(from)d(the)i(base)g(set)g(b)o (y)g(giving)e(a)262 1612 y(concrete)g(n)o(umerical)c(de\014nition)i(to) g(the)h(in)o(tuitiv)o(e)f(notions)g(of)f(h)o(ub)h(and)g(authorit)o(y)g (from)262 1662 y(the)g(b)q(eginning)g(of)f(this)h(section.)h(The)f (algorithm)e(asso)q(ciates)j(a)f(non-negativ)o(e)g Fh(authority)262 1712 y(weight)g Fd(x)413 1718 y Fe(p)445 1712 y Fn(and)h(a)f (non-negativ)o(e)g Fh(hub)i(weight)e Fd(y)1028 1718 y Fe(p)1062 1712 y Fn(with)g(eac)o(h)h(page)g Fd(p)d Ff(2)g Fd(V)f Fn(.)j(W)m(e)g(will)f(only)262 1762 y(b)q(e)g(in)o(terested)i (in)d(the)h Fh(r)n(elative)f Fn(v)n(alues)h(of)f(these)i(w)o(eigh)o (ts,)f(not)f(their)i(actual)e(magnitudes;)262 1812 y(so)j(in)g(the)h (manipulation)d(of)h(the)j(w)o(eigh)o(ts,)e(w)o(e)g(apply)g(a)g (normalization)e(to)i(prev)o(en)o(t)i(the)262 1861 y(w)o(eigh)o(ts)11 b(from)e(o)o(v)o(er\015o)o(wing.)h(\(The)h(actual)g(c)o(hoice)h(of)e (normalization)f(do)q(es)j(not)f(a\013ect)h(the)262 1911 y(results;)k(w)o(e)g(main)o(tain)c(the)k(in)o(v)n(arian)o(t)e(that)i (the)g(squares)h(of)e(all)f(w)o(eigh)o(ts)h(sum)g(to)g(1.\))g(A)262 1961 y(page)f Fd(p)h Fn(with)g(a)f(large)h(w)o(eigh)o(t)f Fd(x)785 1967 y Fe(p)819 1961 y Fn(\(resp.)i Fd(y)956 1967 y Fe(p)975 1961 y Fn(\))f(will)f(b)q(e)h(view)o(ed)g(as)g(a)g(\\b) q(etter")h(authorit)o(y)262 2011 y(\(resp.)f(h)o(ub\).)g(Since)g(w)o(e) g(do)g(not)g(imp)q(ose)f(an)o(y)g Fh(a)i(priori)e Fn(estimates,)g(all)g Fd(x)p Fn(-)g(and)h Fd(y)q Fn(-v)n(alues)262 2061 y(are)g(set)i(to)e(a) g(uniform)e(constan)o(t)j(initially)m(.)c(As)k(will)e(b)q(e)i(seen)h (later,)e(ho)o(w)o(ev)o(er,)g(the)h(\014nal)262 2110 y(results)f(are)f(essen)o(tially)g(una\013ected)h(b)o(y)f(this)g (initialization.)324 2175 y(The)i(authorit)o(y)e(and)i(h)o(ub)f(w)o (eigh)o(ts)g(are)h(up)q(dated)g(as)f(follo)o(ws.)f(If)h(a)g(page)g(is)g (p)q(oin)o(ted)262 2225 y(to)g(b)o(y)f(man)o(y)g(go)q(o)q(d)h(h)o(ubs,) g(w)o(e)g(w)o(ould)f(lik)o(e)h(to)g(increase)h(its)f(authorit)o(y)g(w)o (eigh)o(t;)f(th)o(us)i(for)262 2274 y(a)e(page)h Fd(p)p Fn(,)g(the)g(v)n(alue)g(of)f Fd(x)696 2280 y Fe(p)730 2274 y Fn(is)h(up)q(dated)h(to)e(b)q(e)i(to)f(b)q(e)h(the)f(sum)f(of)h Fd(y)1386 2280 y Fe(q)1419 2274 y Fn(o)o(v)o(er)g(all)f(pages)h Fd(q)262 2324 y Fn(that)e(link)g(to)h Fd(p)p Fn(:)780 2423 y Fd(x)804 2429 y Fe(p)834 2423 y Fn(=)973 2384 y Fc(X)878 2473 y Fe(q)h Fm(suc)o(h)g(that)e Fe(q)q Fb(!)p Fe(p)1134 2423 y Fd(y)1154 2429 y Fe(q)1173 2423 y Fd(;)464 b Fn(\(1\))p eop %%Page: 5 5 5 4 bop 262 224 a Fn(where)15 b(the)g(notation)f Fd(q)g Ff(!)e Fd(p)i Fn(indicates)h(that)g Fd(q)g Fn(links)f(to)g Fd(p)p Fn(.)g(In)h(a)f(strictly)h(dual)f(fashion,)262 274 y(if)f(a)g(page)h(p)q(oin)o(ts)g(to)g(man)o(y)e(go)q(o)q(d)h (authorities,)g(its)h(h)o(ub)g(w)o(eigh)o(t)g(is)f(increased)j(via)780 378 y Fd(y)800 384 y Fe(p)831 378 y Fn(=)969 339 y Fc(X)875 428 y Fe(q)f Fm(suc)o(h)f(that)g Fe(p)p Fb(!)p Fe(q)1130 378 y Fd(x)1154 384 y Fe(q)1173 378 y Fd(:)464 b Fn(\(2\))262 520 y(There)16 b(is)f(a)h(more)e(compact)h(w)o(a)o(y)f(to)i(write)f (these)i(up)q(dates,)f(and)g(it)f(turns)h(out)f(to)h(shed)262 569 y(more)e(ligh)o(t)g(on)g(the)i(mathematical)c(pro)q(cess.)k(Let)g (us)f(n)o(um)o(b)q(er)g(the)g(pages)h Ff(f)p Fn(1)p Fd(;)7 b Fn(2)p Fd(;)g(:)g(:)g(:)s(;)g(n)p Ff(g)262 619 y Fn(and)13 b(de\014ne)h(their)g Fh(adjac)n(ency)h(matrix)e Fd(A)g Fn(to)h(b)q(e)g(the)g Fd(n)8 b Ff(\002)g Fd(n)13 b Fn(matrix)f(whose)i (\()p Fd(i;)7 b(j)r Fn(\)th)14 b(en)o(try)262 669 y(is)k(equal)h(to)g (1)g(if)f(page)h Fd(i)h Fn(links)e(to)h(page)g Fd(j)r Fn(,)g(and)g(is)g(0)g(otherwise.)h(Let)f(us)h(also)e(write)262 719 y(the)j(set)g(of)f(all)f Fd(x)p Fn(-v)n(alues)g(as)i(a)f(v)o(ector) h Fd(x)h Fn(=)h(\()p Fd(x)1067 725 y Fm(1)1085 719 y Fd(;)7 b(x)1128 725 y Fm(2)1146 719 y Fd(;)g(:)g(:)g(:)e(;)i(x)1263 725 y Fe(n)1285 719 y Fn(\),)20 b(and)g(similarly)d(de\014ne)262 769 y Fd(y)j Fn(=)f(\()p Fd(y)389 775 y Fm(1)408 769 y Fd(;)7 b(y)447 775 y Fm(2)465 769 y Fd(;)g(:)g(:)g(:)e(;)i(y)578 775 y Fe(n)600 769 y Fn(\).)18 b(Then)h(the)g(up)q(date)f(rule)h(for)e Fd(x)h Fn(can)g(b)q(e)h(written)g(as)f Fd(x)g Ff( )g Fd(A)1654 754 y Fe(T)1681 769 y Fd(y)262 819 y Fn(and)c(the)g(up)q (date)h(rule)g(for)e Fd(y)j Fn(can)f(b)q(e)f(written)h(as)f Fd(y)g Ff( )e Fd(Ax)p Fn(.)h(Un)o(winding)g(these)j(one)e(step)262 868 y(further,)g(w)o(e)g(ha)o(v)o(e)710 929 y Fd(x)d Ff( )g Fd(A)829 912 y Fe(T)856 929 y Fd(y)i Ff( )e Fd(A)973 912 y Fe(T)999 929 y Fd(Ax)h Fn(=)g(\()p Fd(A)1157 912 y Fe(T)1183 929 y Fd(A)p Fn(\))p Fd(x)395 b Fn(\(3\))262 1014 y(and)719 1075 y Fd(y)14 b Ff( )d Fd(Ax)g Ff( )g Fd(AA)987 1057 y Fe(T)1013 1075 y Fd(y)j Fn(=)e(\()p Fd(AA)1169 1057 y Fe(T)1195 1075 y Fn(\))p Fd(y)q(:)405 b Fn(\(4\))262 1160 y(Th)o(us)12 b(the)i(v)o(ector)f Fd(x)f Fn(after)h(m)o(ultiple)d(iterations)j(is)f(precisely)i(the)f (result)h(of)e(applying)f(the)262 1210 y Fh(p)n(ower)g(iter)n(ation)g Fn(tec)o(hnique)h(to)f Fd(A)806 1195 y Fe(T)832 1210 y Fd(A)g Fn(|)g(w)o(e)g(m)o(ultiply)d(our)k(initial)d(iterate)j(b)o(y)e (larger)i(and)262 1260 y(larger)f(p)q(o)o(w)o(ers)i(of)e Fd(A)589 1245 y Fe(T)615 1260 y Fd(A)h Fn(|)f(and)h(a)g(standard)g (result)g(in)g(linear)f(algebra)g(tells)h(us)g(that)g(this)262 1309 y(sequence)k(of)d(iterates,)h(when)g(normalized,)e(con)o(v)o (erges)j(to)f(the)g(principal)f(eigen)o(v)o(ector)i(of)262 1359 y Fd(A)293 1344 y Fe(T)319 1359 y Fd(A)p Fn(.)e(Similarly)l(,)e (the)j(sequence)i(of)d(v)n(alues)g(for)g(the)i(normalized)d(v)o(ector)i Fd(y)i Fn(con)o(v)o(erges)f(to)262 1409 y(the)d(principal)f(eigen)o(v)o (ector)i(of)f Fd(AA)824 1394 y Fe(T)850 1409 y Fn(.)g(\(See)h(the)g(b)q (o)q(ok)e(b)o(y)h(Golub)f(and)h(V)m(an)g(Loan)f([18])g(for)262 1459 y(bac)o(kground)i(on)h(eigen)o(v)o(ectors)h(and)f(p)q(o)o(w)o(er)g (iteration.\))324 1512 y(In)19 b(fact,)f(p)q(o)o(w)o(er)i(iteration)e (will)g(con)o(v)o(erge)i(to)e(the)i(principal)e(eigen)o(v)o(ector)i (for)f(an)o(y)262 1562 y(\\non-degenerate")g(c)o(hoice)g(of)e(initial)g (v)o(ector)i(|)e(in)h(our)h(case,)f(for)g(example,)f(for)h(an)o(y)262 1612 y(v)o(ector)g(all)e(of)h(whose)h(en)o(tries)g(are)g(p)q(ositiv)o (e.)f(This)g(sa)o(ys)h(that)f(the)h(h)o(ub)g(and)f(authorit)o(y)262 1662 y(w)o(eigh)o(ts)12 b(computed)g(are)h(truly)f(an)g Fh(intrinsic)g Fn(feature)h(of)f(the)h(collection)f(of)g(link)o(ed)g (pages,)262 1711 y(not)h(an)h(artifact)f(of)g(the)i(c)o(hoice)f(of)f (initial)f(w)o(eigh)o(ts)i(or)g(the)g(tuning)f(of)h(arbitrary)f(param-) 262 1761 y(eters.)h(In)o(tuitiv)o(ely)m(,)e(the)i(pages)g(with)g(large) f(w)o(eigh)o(ts)h(represen)o(t)i(a)d(v)o(ery)h(\\dense")h(pattern)262 1811 y(of)h(link)n(age,)g(from)f(pages)j(of)f(large)g(h)o(ub)g(w)o (eigh)o(t)g(to)g(pages)h(of)f(large)g(authorit)o(y)f(w)o(eigh)o(t.)262 1861 y(This)h(t)o(yp)q(e)i(of)e(structure)k(|)c(a)h(densely)h(link)o (ed)e Fh(c)n(ommunity)i Fn(of)e(thematically)f(related)262 1911 y(h)o(ubs)e(and)f(authorities)h(|)g(will)e(b)q(e)j(the)f(motiv)n (ation)d(underlying)i(Section)i(2.2)e(b)q(elo)o(w.)324 1964 y(Finally)m(,)g(the)k(output)g(of)e(HITS)i(algorithm)c(for)j(the)h (giv)o(en)e(searc)o(h)j(topic)e(is)g(a)g(short)262 2014 y(list)d(consisting)h(of)f(the)i(pages)f(with)f(the)i(largest)f(h)o(ub) g(w)o(eigh)o(ts)g(and)f(the)i(pages)f(with)g(the)262 2064 y(largest)g(authorit)o(y)h(w)o(eigh)o(ts.)f(Th)o(us)h(the)g (algorithm)d(has)j(the)g(follo)o(wing)d(in)o(teresting)k(fea-)262 2113 y(ture:)11 b(after)g(using)f(the)i(query)f(terms)g(to)f(collect)h (the)h(ro)q(ot)f(set,)g(the)g(algorithm)e(completely)262 2163 y(ignores)15 b(textual)g(con)o(ten)o(t)h(thereafter.)h(In)e(other) h(w)o(ords,)f(HITS)h(is)f(a)g(purely)h(link-based)262 2213 y(computation)9 b(once)k(the)f(ro)q(ot)g(set)g(has)g(b)q(een)h (assem)o(bled,)d(with)h(no)h(further)g(regard)g(to)g(the)262 2263 y(query)i(terms.)f(Nev)o(ertheless,)j(HITS)e(pro)o(vides)h (surprisingly)e(go)q(o)q(d)h(searc)o(h)h(results)g(for)f(a)262 2313 y(wide)j(range)g(of)f(queries.)i(F)m(or)e(instance,)i(when)f (tested)i(on)e(the)g(sample)f(query)i(\\searc)o(h)262 2363 y(engines",)c(the)h(top)g(authorities)f(returned)j(b)o(y)d(HITS)h (w)o(ere)g(Y)m(aho)q(o!,)e(Excite,)i(Magellan,)262 2412 y(Lycos,)i(and)g(AltaVista)g(|)f(ev)o(en)i(though)f(none)h(of)f(these)h (pages)g(\(at)f(the)h(time)e(of)h(the)262 2462 y(exp)q(erimen)o(t\))c (con)o(tained)h(the)h(phrase)g(\\searc)o(h)f(engines.")p eop %%Page: 6 6 6 5 bop 324 224 a Fn(In)18 b(subsequen)o(t)h(w)o(ork)f([5,)6 b(9,)g(10],)16 b(the)j(HITS)f(algorithm)d(has)j(b)q(een)h(generalized)g (b)o(y)262 274 y(mo)q(difying)14 b(the)k(en)o(tries)h(of)e Fd(A)h Fn(so)g(that)g(they)g(are)g(no)f(longer)h(b)q(o)q(olean.)f (These)h(mo)q(di\014-)262 324 y(cations)d(tak)o(e)g(in)o(to)g(accoun)o (t)g(the)h(con)o(ten)o(t)g(of)f(the)h(pages)f(in)g(the)h(base)g(set,)g (the)g(in)o(ternet)262 374 y(domains)d(in)h(whic)o(h)h(they)g(reside,)h (and)f(so)g(on.)f(Nev)o(ertheless,)j(most)d(of)g(these)i(mo)q (di\014ca-)262 423 y(tions)d(retain)h(the)g(basic)g(p)q(o)o(w)o(er)g (iteration)f(pro)q(cess)i(and)f(the)g(in)o(terpretation)g(of)f(h)o(ub)h (and)262 473 y(authorit)o(y)f(scores)i(as)f(comp)q(onen)o(ts)g(of)f(a)h (principal)f(eigen)o(v)o(ector,)h(as)g(ab)q(o)o(v)o(e.)262 598 y Fg(2.2)47 b(T)l(ra)o(wling)14 b(the)h(W)l(eb)h(for)f(cyb)q (er-comm)o(uniti)o(es)262 681 y Fn(In)g(this)g(section)h(w)o(e)f(turn)h (to)f(a)g(second)h(algorithm)d(dev)o(elop)q(ed)i(for)g(the)h(W)m(eb)f (graph.)f(In)262 730 y(con)o(trast)d(to)f(HITS,)h(whic)o(h)f(is)h(a)f (searc)o(h)i(algorithm)c(designed)j(to)g(\014nd)g(high-qualit)o(y)d (pages)262 780 y(ab)q(out)14 b(a)f(\014xed)i(topic,)e(the)i Fh(tr)n(aw)r(ling)i Fn(algorithm)11 b(describ)q(ed)16 b(b)q(elo)o(w)e(seeks)h(to)f(en)o(umerate)262 830 y Fh(al)r(l)20 b Fn(topics)e(\(under)g(a)f(certain)g(de\014nition\),)g(and)g (therefore)h(pro)q(cesses)i(the)e(en)o(tire)g(W)m(eb)262 880 y(graph.)324 930 y(W)m(e)e(b)q(egin)h(with)g(a)f(more)g(concrete)j (de\014nition)d(of)h(the)g(t)o(yp)q(es)h(of)e(topic)h(w)o(e)g(wish)g (to)262 979 y(en)o(umerate.)10 b(Recall)h(that)h(a)f(complete)f (bipartite)i(clique)f Fd(K)1207 985 y Fe(i;j)1258 979 y Fn(is)g(a)g(graph)g(in)g(whic)o(h)h(ev)o(ery)262 1029 y(one)f(of)f Fd(i)i Fn(no)q(des)g(has)f(an)g(edge)h(directed)g(to)f (eac)o(h)h(of)e Fd(j)k Fn(no)q(des)e(\(in)e(the)i(follo)o(wing)d (treatmen)o(t)262 1079 y(it)15 b(is)i(simplest)e(to)h(think)g(of)g(the) h(\014rst)g Fd(i)f Fn(no)q(des)h(as)g(b)q(eing)f(distinct)h(from)d(the) j(second)g Fd(j)r Fn(;)262 1129 y(in)f(fact)i(this)f(is)g(not)h(essen)o (tial)f(to)h(our)f(algorithms)e(or)i(mo)q(dels\).)f(W)m(e)h(further)h (de\014ne)h(a)262 1179 y Fh(bip)n(artite)c(c)n(or)n(e)g Fd(C)545 1185 y Fe(i;j)599 1179 y Fn(to)g(b)q(e)h(a)f(graph)h(on)f Fd(i)10 b Fn(+)h Fd(j)18 b Fn(no)q(des)e(that)f(con)o(tains)h(at)f (least)g(one)h Fd(K)1663 1185 y Fe(i;j)262 1229 y Fn(as)j(a)g (subgraph.)h(The)g(in)o(tuition)e(motiv)n(ating)e(this)k(notion)f(is)g (the)h(follo)o(wing:)d(on)i(an)o(y)262 1278 y(su\016cien)o(tly)14 b(w)o(ell)g(represen)o(ted)k(topic)d(on)g(the)g(W)m(eb,)f(there)i(will) e(\(for)g(some)g(appropriate)262 1328 y(v)n(alues)g(of)h Fd(i)g Fn(and)g Fd(j)r Fn(\))g(b)q(e)h(a)e(bipartite)h(core)h(in)e(the) i(W)m(eb)f(graph.)f(Figure)h(1)g(illustrates)g(an)262 1378 y(instance)j(of)f(a)h Fd(C)547 1384 y Fm(4)p Fe(;)p Fm(3)610 1378 y Fn(in)f(whic)o(h)h(the)g(four)g(no)q(des)h(on)e(the)i (left)e(ha)o(v)o(e)h(h)o(yp)q(erlinks)g(to)g(the)262 1428 y(home)11 b(pages)j(of)e(three)i(ma)r(jor)e(commercial)e(aircraft) j(man)o(ufacturers.)f(Suc)o(h)h(a)g(subgraph)p 526 1532 912 2 v 526 2144 2 613 v 540 2132 a @beginspecial 156 @llx 419 @lly 368 @urx 560 @ury 2120 @rwi @setspecial %%BeginDocument: fig1.ps /IdrawDict 51 dict def IdrawDict begin /reencodeISO { dup dup findfont dup length dict begin { 1 index /FID ne { def }{ pop pop } ifelse } forall /Encoding ISOLatin1Encoding def currentdict end definefont } def /ISOLatin1Encoding [ /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /space/exclam/quotedbl/numbersign/dollar/percent/ampersand/quoteright /parenleft/parenright/asterisk/plus/comma/minus/period/slash /zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon /less/equal/greater/question/at/A/B/C/D/E/F/G/H/I/J/K/L/M/N /O/P/Q/R/S/T/U/V/W/X/Y/Z/bracketleft/backslash/bracketright /asciicircum/underscore/quoteleft/a/b/c/d/e/f/g/h/i/j/k/l/m /n/o/p/q/r/s/t/u/v/w/x/y/z/braceleft/bar/braceright/asciitilde /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef/.notdef /.notdef/dotlessi/grave/acute/circumflex/tilde/macron/breve /dotaccent/dieresis/.notdef/ring/cedilla/.notdef/hungarumlaut /ogonek/caron/space/exclamdown/cent/sterling/currency/yen/brokenbar /section/dieresis/copyright/ordfeminine/guillemotleft/logicalnot /hyphen/registered/macron/degree/plusminus/twosuperior/threesuperior /acute/mu/paragraph/periodcentered/cedilla/onesuperior/ordmasculine /guillemotright/onequarter/onehalf/threequarters/questiondown /Agrave/Aacute/Acircumflex/Atilde/Adieresis/Aring/AE/Ccedilla /Egrave/Eacute/Ecircumflex/Edieresis/Igrave/Iacute/Icircumflex /Idieresis/Eth/Ntilde/Ograve/Oacute/Ocircumflex/Otilde/Odieresis /multiply/Oslash/Ugrave/Uacute/Ucircumflex/Udieresis/Yacute /Thorn/germandbls/agrave/aacute/acircumflex/atilde/adieresis /aring/ae/ccedilla/egrave/eacute/ecircumflex/edieresis/igrave /iacute/icircumflex/idieresis/eth/ntilde/ograve/oacute/ocircumflex /otilde/odieresis/divide/oslash/ugrave/uacute/ucircumflex/udieresis /yacute/thorn/ydieresis ] def /Helvetica-Bold reencodeISO def /arrowHeight 8 def /arrowWidth 4 def /none null def /numGraphicParameters 17 def /stringLimit 65535 def /Begin { save numGraphicParameters dict begin } def /End { end restore } def /SetB { dup type /nulltype eq { pop false /brushRightArrow idef false /brushLeftArrow idef true /brushNone idef } { /brushDashOffset idef /brushDashArray idef 0 ne /brushRightArrow idef 0 ne /brushLeftArrow idef /brushWidth idef false /brushNone idef } ifelse } def /SetCFg { /fgblue idef /fggreen idef /fgred idef } def /SetCBg { /bgblue idef /bggreen idef /bgred idef } def /SetF { /printSize idef /printFont idef } def /SetP { dup type /nulltype eq { pop true /patternNone idef } { dup -1 eq { /patternGrayLevel idef /patternString idef } { /patternGrayLevel idef } ifelse false /patternNone idef } ifelse } def /BSpl { 0 begin storexyn newpath n 1 gt { 0 0 0 0 0 0 1 1 true subspline n 2 gt { 0 0 0 0 1 1 2 2 false subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 2 copy false subspline } if n 2 sub dup n 1 sub dup 2 copy 2 copy false subspline patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Circ { newpath 0 360 arc patternNone not { ifill } if brushNone not { istroke } if } def /CBSpl { 0 begin dup 2 gt { storexyn newpath n 1 sub dup 0 0 1 1 2 2 true subspline 1 1 n 3 sub { /i exch def i 1 sub dup i dup i 1 add dup i 2 add dup false subspline } for n 3 sub dup n 2 sub dup n 1 sub dup 0 0 false subspline n 2 sub dup n 1 sub dup 0 0 1 1 false subspline patternNone not { ifill } if brushNone not { istroke } if } { Poly } ifelse end } dup 0 4 dict put def /Elli { 0 begin newpath 4 2 roll translate scale 0 0 1 0 360 arc patternNone not { ifill } if brushNone not { istroke } if end } dup 0 1 dict put def /Line { 0 begin 2 storexyn newpath x 0 get y 0 get moveto x 1 get y 1 get lineto brushNone not { istroke } if 0 0 1 1 leftarrow 0 0 1 1 rightarrow end } dup 0 4 dict put def /MLine { 0 begin storexyn newpath n 1 gt { x 0 get y 0 get moveto 1 1 n 1 sub { /i exch def x i get y i get lineto } for patternNone not brushLeftArrow not brushRightArrow not and and { ifill } if brushNone not { istroke } if 0 0 1 1 leftarrow n 2 sub dup n 1 sub dup rightarrow } if end } dup 0 4 dict put def /Poly { 3 1 roll newpath moveto -1 add { lineto } repeat closepath patternNone not { ifill } if brushNone not { istroke } if } def /Rect { 0 begin /t exch def /r exch def /b exch def /l exch def newpath l b moveto l t lineto r t lineto r b lineto closepath patternNone not { ifill } if brushNone not { istroke } if end } dup 0 4 dict put def /Text { ishow } def /idef { dup where { pop pop pop } { exch def } ifelse } def /ifill { 0 begin gsave patternGrayLevel -1 ne { fgred bgred fgred sub patternGrayLevel mul add fggreen bggreen fggreen sub patternGrayLevel mul add fgblue bgblue fgblue sub patternGrayLevel mul add setrgbcolor eofill } { eoclip originalCTM setmatrix pathbbox /t exch def /r exch def /b exch def /l exch def /w r l sub ceiling cvi def /h t b sub ceiling cvi def /imageByteWidth w 8 div ceiling cvi def /imageHeight h def bgred bggreen bgblue setrgbcolor eofill fgred fggreen fgblue setrgbcolor w 0 gt h 0 gt and { l b translate w h scale w h true [w 0 0 h neg 0 h] { patternproc } imagemask } if } ifelse grestore end } dup 0 8 dict put def /istroke { gsave brushDashOffset -1 eq { [] 0 setdash 1 setgray } { brushDashArray brushDashOffset setdash fgred fggreen fgblue setrgbcolor } ifelse brushWidth setlinewidth originalCTM setmatrix stroke grestore } def /ishow { 0 begin gsave fgred fggreen fgblue setrgbcolor printFont printSize scalefont setfont /descender 0 printFont /FontBBox get 1 get printFont /FontMatrix get transform exch pop def /vertoffset 1 printSize sub descender sub def { 0 vertoffset moveto show /vertoffset vertoffset printSize sub def } forall grestore end } dup 0 2 dict put def /patternproc { 0 begin /patternByteLength patternString length def /patternHeight patternByteLength 8 mul sqrt cvi def /patternWidth patternHeight def /patternByteWidth patternWidth 8 idiv def /imageByteMaxLength imageByteWidth imageHeight mul stringLimit patternByteWidth sub min def /imageMaxHeight imageByteMaxLength imageByteWidth idiv patternHeight idiv patternHeight mul patternHeight max def /imageHeight imageHeight imageMaxHeight sub store /imageString imageByteWidth imageMaxHeight mul patternByteWidth add string def 0 1 imageMaxHeight 1 sub { /y exch def /patternRow y patternByteWidth mul patternByteLength mod def /patternRowString patternString patternRow patternByteWidth getinterval def /imageRow y imageByteWidth mul def 0 patternByteWidth imageByteWidth 1 sub { /x exch def imageString imageRow x add patternRowString putinterval } for } for imageString end } dup 0 12 dict put def /min { dup 3 2 roll dup 4 3 roll lt { exch } if pop } def /max { dup 3 2 roll dup 4 3 roll gt { exch } if pop } def /arrowhead { 0 begin transform originalCTM itransform /taily exch def /tailx exch def transform originalCTM itransform /tipy exch def /tipx exch def /dy tipy taily sub def /dx tipx tailx sub def /angle dx 0 ne dy 0 ne or { dy dx atan } { 90 } ifelse def gsave originalCTM setmatrix tipx tipy translate angle rotate newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath patternNone not { originalCTM setmatrix /padtip arrowHeight 2 exp 0.25 arrowWidth 2 exp mul add sqrt brushWidth mul arrowWidth div def /padtail brushWidth 2 div def tipx tipy translate angle rotate padtip 0 translate arrowHeight padtip add padtail add arrowHeight div dup scale arrowheadpath ifill } if brushNone not { originalCTM setmatrix tipx tipy translate angle rotate arrowheadpath istroke } if grestore end } dup 0 9 dict put def /arrowheadpath { newpath 0 0 moveto arrowHeight neg arrowWidth 2 div lineto arrowHeight neg arrowWidth 2 div neg lineto closepath } def /leftarrow { 0 begin y exch get /taily exch def x exch get /tailx exch def y exch get /tipy exch def x exch get /tipx exch def brushLeftArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /rightarrow { 0 begin y exch get /tipy exch def x exch get /tipx exch def y exch get /taily exch def x exch get /tailx exch def brushRightArrow { tipx tipy tailx taily arrowhead } if end } dup 0 4 dict put def /midpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 x1 add 2 div y0 y1 add 2 div end } dup 0 4 dict put def /thirdpoint { 0 begin /y1 exch def /x1 exch def /y0 exch def /x0 exch def x0 2 mul x1 add 3 div y0 2 mul y1 add 3 div end } dup 0 4 dict put def /subspline { 0 begin /movetoNeeded exch def y exch get /y3 exch def x exch get /x3 exch def y exch get /y2 exch def x exch get /x2 exch def y exch get /y1 exch def x exch get /x1 exch def y exch get /y0 exch def x exch get /x0 exch def x1 y1 x2 y2 thirdpoint /p1y exch def /p1x exch def x2 y2 x1 y1 thirdpoint /p2y exch def /p2x exch def x1 y1 x0 y0 thirdpoint p1x p1y midpoint /p0y exch def /p0x exch def x2 y2 x3 y3 thirdpoint p2x p2y midpoint /p3y exch def /p3x exch def movetoNeeded { p0x p0y moveto } if p1x p1y p2x p2y p3x p3y curveto end } dup 0 17 dict put def /storexyn { /n exch def /y n array def /x n array def n 1 sub -1 0 { /i exch def y i 3 2 roll put x i 3 2 roll put } for } def %I Idraw 9 Grid 8 Begin %I b u %I cfg u %I cbg u %I f u %I p u %I t [ 0.791209 0 0 0.791209 0 0 ] concat /originalCTM matrix currentmatrix def Begin %I Elli %I b 65535 2 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 76 75 ] concat %I 146 620 10 10 Elli End Begin %I Elli %I b 65535 2 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 76 -26 ] concat %I 146 620 10 10 Elli End Begin %I Elli %I b 65535 2 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 75 25 ] concat %I 146 620 10 10 Elli End Begin %I Elli %I b 65535 2 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 175 -26 ] concat %I 146 620 10 10 Elli End Begin %I Elli %I b 65535 2 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 175 75 ] concat %I 146 620 10 10 Elli End Begin %I Elli %I b 65535 2 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 175 25 ] concat %I 146 620 10 10 Elli End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 35 75 ] concat %I 197 620 277 620 Line End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 35 75 ] concat %I 197 620 277 519 Line End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 35 75 ] concat %I 197 620 277 570 Line End Begin %I Elli %I b 65535 2 0 0 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 75 -76 ] concat %I 146 620 10 10 Elli End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 35 75 ] concat %I 197 570 277 620 Line End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 35 75 ] concat %I 197 570 277 519 Line End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 35 75 ] concat %I 197 519 277 570 Line End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 35 75 ] concat %I 197 570 277 570 Line End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 35 75 ] concat %I 197 519 277 519 Line End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 35 75 ] concat %I 197 469 277 620 Line End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 35 75 ] concat %I 197 519 277 620 Line End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 35 75 ] concat %I 197 469 277 570 Line End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 35 75 ] concat %I 197 469 277 519 Line End Begin %I BSpl %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 35 75 ] concat %I 3 177 620 166 570 177 519 3 BSpl End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-bold-r-*-140-* Helvetica-Bold 14 SetF %I t [ 1 0 0 1 336 702 ] concat %I [ (www.boeing.com) ] Text End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f *-helvetica-bold-r-*-140-* Helvetica-Bold 14 SetF %I t [ 1 0 0 1 337 652 ] concat %I [ (www.airbus.com) ] Text End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 35 75 ] concat %I 187 479 187 509 Line End Begin %I Line %I b 65535 1 0 1 [] 0 SetB %I cfg Black 0 0 0 SetCFg %I cbg White 1 1 1 SetCBg none SetP %I p n %I t [ 1 0 0 1 35 75 ] concat %I 187 610 187 580 Line End Begin %I Text %I cfg Black 0 0 0 SetCFg %I f 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bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff fffffffffff4 bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff fffffffffff4 bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff fffffffffff4 bffffffffffffffffffffffffffffff77ffefffffdffffffffffffffffffffffffffffff fffffffffff4 bffffffffffffffffffffffffffffff37ffefffffbffffdfffffffffffffffffffffffff fffffffffff4 bffffffffffffffffffffffffffffff35a06398f31f3988cc47fffffffffffffffffffff fffffffffff4 bffffffffffffffffffffffffffffff55adad6bedbed6b5b5bffffffffffffffffffffff fffffffffff4 bffffffffffffffffffffffffffffff65adad0bedbef0b585cffffffffffffffffffffff fffffffffff4 bffffffffffffffffffffffffffffff65adad7bedbed7b5bdf7fffffffffffffffffffff fffffffffff4 bffffffffffffffffffffffffffffff762da38bf3bf38b4c58ffffffffffffffffffffff fffffffffff4 bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff fffffffffff4 bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff fffffffffff4 bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff fffffffffff4 bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff fffffffffff4 bfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff fffffffffff4 800000000000000000000000000000000000000000000000000000000000000000000000 000000000004 ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff fffffffffffc showpage % stop using temporary dictionary end % restore original state origstate restore %%EndDocument @endspecial 1690 1544 V 272 1546 1420 2 v 656 1619 a Fj(Fig.)7 b(5.)13 b Fk(Core)g(distribution)k(b)o(y)c(righ)o(t)h(side.) 262 1863 y Fg(3.3)47 b(Connectivit)o(y)13 b(of)j(lo)q(cal)f(subgraphs) 262 1964 y Fn(W)m(e)j(no)o(w)h(consider)h(some)e(relating)g(to)h(the)h (connectivit)o(y)f(of)f(lo)q(cal)h(subgraphs)g(of)g(the)262 2014 y(W)m(eb)d(graph.)g(W)m(e)g(b)q(egin)h(b)o(y)g(\014xing)f(our)g (set)i(of)e(lo)q(cal)g(subgraphs)h(to)g(b)q(e)g(the)h(base)f(sets)262 2064 y(arising)g(in)h(the)h(HITS)g(algorithm)d(of)h(Section)i(2.)f(T)m (o)g(recapitulate,)g(w)o(e)h(b)q(egin)f(with)g Fd(c)262 2113 y Fn(no)q(des)f(obtained)g(b)o(y)f(issuing)g(a)h(k)o(eyw)o(ord)f (query)i(to)e(a)h(text-based)g(searc)o(h)h(engine.)f(W)m(e)262 2163 y(then)12 b(expand)h(this)f(ro)q(ot)g(set)h(to)f(the)h(base)g(set) g(b)o(y)f(adding)f(an)o(y)h(page)g(link)o(ed)g(to)g(b)o(y)g(a)f(page) 262 2213 y(in)h(the)i(ro)q(ot)e(set,)i(and)f(an)o(y)f(page)h(linking)e (to)i(a)g(page)f(in)h(the)g(ro)q(ot)g(set)h(\(up)f(to)g(a)g(cut-o\013)g (of)262 2263 y Fd(d)g Fn(pages)i(p)q(er)g(elemen)o(t)f(of)g(the)h(ro)q (ot)f(set\).)h(In)g(exp)q(erimen)o(ts,)f(w)o(e)g(ha)o(v)o(e)h(applied)e (this)i(with)262 2313 y Fd(c)p Fn(,)c(the)i(size)g(of)f(the)h(ro)q(ot)f (set,)h(equal)f(to)g(200;)f(and)h Fd(d)p Fn(,)f(the)i(cut-o\013,)f (equal)g(to)g(50.)f(As)i(ab)q(o)o(v)o(e,)262 2363 y(the)g(resulting)f (base)h(set)h(t)o(ypically)d(consists)j(of)e(roughly)f(1000)h(to)g (3000)g(pages,)g(and)h(since)262 2412 y(w)o(e)i(wish)h(to)g(fo)q(cus)g (on)f(cross-site)i(links)f(w)o(e)g(discard)g(links)f(b)q(et)o(w)o(een)i (t)o(w)o(o)e(pages)h(within)262 2462 y(the)e(same)f(site.)p eop %%Page: 12 12 12 11 bop 324 224 a Fn(W)m(e)15 b(no)o(w)h(ask)f(ho)o(w)h(w)o (ell-connected)h(these)g(lo)q(cal)e(subgraphs)i(are.)e(W)m(e)h(will)e (view)i Fd(G)262 274 y Fn(primarily)h(as)j(a)g(directed)h(graph,)e(but) h(w)o(e)h(also)e(de\014ne)i(the)g(undirected)g(v)o(ersion)f Fd(G)1681 280 y Fe(u)262 324 y Fn(obtained)13 b(b)o(y)h(ignoring)e(the) j(direction)f(of)f(all)g(edges.)324 376 y(A)f(collection)f(of)g(graphs) i(constructed)h(in)d(this)h(w)o(a)o(y)f(for)h(an)f(ensem)o(ble)h(of)f (\014ft)o(y)h(sample)262 426 y(query)18 b(terms)f(rev)o(eals)i(some)e (consisten)o(tly)h(o)q(ccurring)g(structural)h(prop)q(erties;)g(w)o(e)f (will)262 476 y(discuss)d(sev)o(eral)f(of)f(these)j(here)f(at)e(a)h (qualitativ)o(e)e(lev)o(el.)262 590 y Fh(A)j(r)n(ange)g(of)g(c)n(onne)n (ctivity)h(r)n(elations.)k Fn(A)14 b(\014rst)h(observ)n(ation)f(is)h (that)f(the)h(graphs)f Fd(G)1611 596 y Fe(u)1647 590 y Fn(are)262 640 y(not,)i(in)g(general,)g(connected.)i(This)f(is)f(in)o (tuitiv)o(ely)f(v)o(ery)i(natural:)f(the)h(initial)e(ro)q(ot)h(set)262 690 y(t)o(ypically)c(induces)i(v)o(ery)g(few)g(edges;)g(and)f(while)g (the)h(expansion)g(to)f(the)h(base)g(set)h(serv)o(es)262 740 y(to)e(connect)i(man)o(y)d(of)i(these)h(no)q(des,)f(others)h (remain)e(in)g(small)f(isolated)h(comp)q(onen)o(ts.)324 792 y(A)d(graph)f Fd(G)511 798 y Fe(u)542 792 y Fn(of)g(this)h(form,)e (ho)o(w)o(ev)o(er,)h(do)q(es)i(t)o(ypically)d(con)o(tain)h(a)h(\\gian)o (t)e(comp)q(onen)o(t")262 842 y(|)j(a)h(connected)h(comp)q(onen)o(t)f (that)g(con)o(tains)g(a)f(signi\014can)o(t)h(constan)o(t)g(fraction)g (of)f(all)g(the)262 892 y(no)q(des.)16 b(In)h(all)e(the)j(cases)f (considered,)h(there)g(w)o(as)e(only)g(a)g(single)h(gian)o(t)e(comp)q (onen)o(t)h(of)262 942 y Fd(G)295 948 y Fe(u)316 942 y Fn(.)324 994 y(T)m(urning)e(to)h(a)g(stronger)i(measure,)e(w)o(e)g (consider)h Fh(bic)n(onne)n(ctivity)t Fn(:)f(w)o(e)g(sa)o(y)h(that)f(t) o(w)o(o)262 1044 y(no)q(des)k Fd(u)g Fn(and)f Fd(v)j Fn(are)e Fh(bic)n(onne)n(cte)n(d)24 b Fn(if)18 b(there)i(is)f(no)g (third)f(no)q(de)i Fd(w)f Fn(so)g(that)g Fd(w)h Fn(lies)f(on)262 1094 y(all)c Fd(u)p Fn(-)p Fd(v)j Fn(paths.)e(W)m(e)g(will)g(call)f (the)j(equiv)n(alence)e(classes)i(of)e(no)q(des)i(under)f(this)g (relation)262 1144 y(the)g Fh(bic)n(onne)n(cte)n(d)h(c)n(omp)n(onents)p Fn(.)f(The)g(graph)f Fd(G)1036 1150 y Fe(u)1074 1144 y Fn(t)o(ypically)f(has)h(a)h(\\gian)o(t)e(biconnected)262 1194 y(comp)q(onen)o(t,")d(again)g(unique.)h(Th)o(us,)g(w)o(e)h(can)f (in)o(tuitiv)o(ely)f(picture)j(the)f(structure)h(of)e Fd(G)1681 1200 y Fe(u)262 1244 y Fn(as)18 b(consisting)h(of)f(a)g(cen)o (tral)h(biconnected)h(\\n)o(ucleus,")f(with)f(small)f(pieces)j (connected)262 1293 y(to)14 b(this)g(n)o(ucleus)i(b)o(y)e(cut-no)q (des,)h(and)f(with)g(other)i(small)c(pieces)j(not)g(connected)h(to)e (this)262 1343 y(n)o(ucleus)g(at)g(all.)324 1396 y(The)19 b(biconnected)i(n)o(ucleus)e(con)o(tains)g(m)o(uc)o(h)f(of)g(the)i(in)o (teresting)g(structure)h(in)d Fd(G)p Fn(;)262 1446 y(for)13 b(example,)f(it)h(generally)g(con)o(tains)h(all)e(the)j(top)e(h)o(ubs)h (and)g(authorities)f(computed)h(b)o(y)262 1495 y(HITS.)f(W)m(e)h(will)f (use)i Fd(H)i Fn(to)d(denote)i(the)f(subgraph)f(of)g Fd(G)g Fn(induced)h(on)f(this)g(biconnected)262 1545 y(n)o(ucleus;)k Fd(H)j Fn(is)c(th)o(us)i(a)f(directed)h(graph,)e(and)h (w)o(e)g(use)h Fd(H)1217 1551 y Fe(u)1256 1545 y Fn(to)f(denote)h(its)f (undirected)262 1595 y(v)o(ersion.)324 1648 y(W)m(e)d(can)h(try)g(to)g (further)g(re\014ne)h(the)f(structure)i(of)d Fd(H)k Fn(b)o(y)c(lo)q (oking)f(at)i Fh(str)n(ongly)g(c)n(on-)262 1698 y(ne)n(cte)n(d)d(c)n (omp)n(onents)p Fn(.)f(In)f(this)h(w)o(e)g(mak)o(e)e(crucial)i(use)g (of)f(the)h(orien)o(tation)f(of)g(edges:)h Fd(u)g Fn(and)262 1747 y Fd(v)i Fn(are)f(related)g(under)h(strong)f(connectivit)o(y)g(if) f(eac)o(h)h(can)g(reac)o(h)g(the)h(other)f(b)o(y)g(a)f(directed)262 1797 y(path.)h(F)m(or)h(this)g(relation,)f(ho)o(w)o(ev)o(er,)g(w)o(e)i (disco)o(v)o(er)f(the)h(follo)o(wing:)c(the)j(subgraphs)h Fd(H)i Fn(do)262 1847 y(not)i(con)o(tain)f(\\gian)o(t)g(strongly)h (connected)i(comp)q(onen)o(ts.")d(Indeed,)h(for)g(man)o(y)e(of)i(the) 262 1897 y(graphs)e(w)o(e)h(considered,)h(the)f(largest)g(strongly)f (connected)i(comp)q(onen)o(t)e(had)g(size)i(less)262 1947 y(than)13 b(20.)324 1999 y(Th)o(us,)c(while)h Fd(G)f Fn(is)h(not)f(connected)j(when)e(view)o(ed)g(in)f(its)h(en)o(tiret)o(y) m(,)g(it)f(can)h(b)q(e)g(view)o(ed)g(as)262 2049 y(ha)o(ving)g(a)h (large)h(subgraph)g(that)f(is)h(biconnected)h(as)e(an)h(undirected)h (graph.)e Fd(G)p Fn(,)g(ho)o(w)o(ev)o(er,)262 2099 y(do)q(es)j(not)g (generally)f(con)o(tain)h(an)o(y)f(large)h(strongly)g(connected)h (subgraphs.)262 2213 y Fh(A)o(lternating)e(c)n(onne)n(ctivity.)19 b Fn(Biconnectivit)o(y)13 b(yielded)g(a)g(gian)o(t)f(comp)q(onen)o(t;)f (strong)i(con-)262 2263 y(nectivit)o(y)e(pulv)o(erized)h(the)g(graph)f (in)o(to)g(tin)o(y)g(comp)q(onen)o(ts.)g(It)g(is)g(natural)g(to)h(ask)f (whether)262 2313 y(there)k(is)f(a)g(natural)g(connectivit)o(y)h (measure)f(that)g(tak)o(es)h(some)e(accoun)o(t)i(of)f(the)h(orien)o (ta-)262 2363 y(tion)e(of)g(edges)i(and)e(still)g(results)i(in)e(large) g(\\comp)q(onen)o(ts.")g(W)m(e)g(no)o(w)g(describ)q(e)j(one)e(suc)o(h) 262 2412 y(measure,)g Fh(alternating)h(c)n(onne)n(ctivity)p Fn(,)f(and)h(observ)o(e)g(a)g(sense)h(in)e(whic)o(h)h(it)f(is)h (di\016cult)f(to)262 2462 y(\014nd)g(the)g(righ)o(t)f(de\014nition)h (of)f(\\comp)q(onen)o(t")g(under)i(this)f(measure.)p eop %%Page: 13 13 13 12 bop 324 224 a Fn(If)11 b Fd(u)h Fn(and)f Fd(v)j Fn(are)e(no)q(des,)g(w)o(e)g(sa)o(y)g(that)f(a)h(sequence)i Fd(P)j Fn(of)11 b(edges)i(in)e Fd(G)h Fn(is)f(an)h Fh(alternating)262 274 y(p)n(ath)19 b Fn(from)f Fd(u)h Fn(to)g Fd(v)i Fn(if)e(\(1\))h Fd(P)k Fn(is)c(a)f(path)g(in)g Fd(G)1045 280 y Fe(u)1086 274 y Fn(with)g(endp)q(oin)o(ts)h Fd(u)f Fn(and)h Fd(v)q Fn(,)f(and)g(\(2\))262 324 y(the)e(orien)o(tations)g(of)f(the)i(edges)g (of)e Fd(P)22 b Fn(strictly)c(alternate)f(in)g Fd(G)p Fn(.)f(Th)o(us,)h Fd(P)22 b Fn(leads)17 b(from)262 374 y Fd(u)g Fn(to)i Fd(v)g Fn(via)f(a)g(sequence)i(of)e(link)f(tra)o(v)o (ersals)i(that)f(alternate)h(forw)o(ard)e(and)i(bac)o(kw)o(ard)262 423 y(directions.)10 b(This)g(de\014nition)g(corresp)q(onds)i(closely)f (to)f(the)h(HITS)f(algorithm.)d(In)o(tuitiv)o(ely)m(,)262 473 y(the)18 b(strict)g(alternation)f(of)g(edge)h(orien)o(tations)f (parallels)g(the)h(w)o(a)o(y)f(in)g(whic)o(h)g(h)o(ub)h(and)262 523 y(authorit)o(y)9 b(w)o(eigh)o(t)h(\015o)o(ws)h(b)q(et)o(w)o(een)h (no)q(des;)e(and)g(indeed,)h(the)g(h)o(ub)f(and)h(authorit)o(y)e(w)o (eigh)o(ts)262 573 y(e\013ectiv)o(ely)h(compute)g(the)g(relativ)o(e)g (gro)o(wth)f(rates)i(of)e(alternating)h(paths)g(from)e(eac)o(h)i(no)q (de.)262 623 y(F)m(urthermore,)g(t)o(w)o(o)h(steps)i(in)e(an)h (alternating)e(path)i(connect)h(t)o(w)o(o)e(no)q(des)h(that)g(either)g (cite)262 672 y(the)k(same)f(page,)g(or)h(are)g(cited)g(b)o(y)f(the)i (same)e(page)g(|)g(this)h(notion)f(of)g(co-citation)g(has)262 722 y(b)q(een)f(used)h(as)f(a)f(similarit)o(y)e(measure)i(among)f(do)q (cumen)o(ts)i([14])e(and)h(among)f(w)o(eb)i(pages)262 772 y(\(e.g.)f([11,)5 b(21,)h(25]\).)324 823 y(Supp)q(ose)13 b(w)o(e)g(write)g Fd(u)f Ff(\030)g Fd(v)i Fn(if)e(there)i(is)e(an)h (alternating)f(path)h(b)q(et)o(w)o(een)h Fd(u)e Fn(and)h Fd(v)q Fn(.)g(It)g(is)262 873 y(clear)f(immedia)o(tely)d(from)i(the)h (de\014nition)g(that)g(the)g(relation)g Ff(\030)g Fn(is)g(symmetric;)e (ho)o(w)o(ev)o(er,)262 923 y(it)i(is)h(easy)g(to)f(construct)j (examples)d(with)g(no)q(des)i Fd(u;)7 b(v)q(;)g(w)12 b Fn(so)h(that)g Fd(u)e Ff(\030)h Fd(v)j Fn(and)d Fd(v)h Ff(\030)f Fd(w)q Fn(,)g(but)262 973 y Fd(u)f Ff(6\030)h Fd(w)q Fn(.)h(As)h(a)g(result,)g Ff(\030)g Fn(is)g(not)g(transitiv)o(e) f(and)h(hence)h(not)f(an)g(equiv)n(alence)g(relation.)324 1024 y(Ho)o(w)o(ev)o(er,)d(w)o(e)h(can)g(sho)o(w)f(a)h(sense)h(in)e (whic)o(h)g Ff(\030)h Fn(is)f(\\nearly")g(an)h(equiv)n(alence)f (relation:)262 1074 y(w)o(e)16 b(can)g(pro)o(v)o(e)f(that)h(if)f(a)h (no)q(de)g Fd(u)f Fn(is)h(related)g(to)g(three)h(no)q(des)g Fd(v)1310 1080 y Fm(1)1328 1074 y Fd(;)7 b(v)1367 1080 y Fm(2)1386 1074 y Fd(;)g(v)1425 1080 y Fm(3)1443 1074 y Fn(,)15 b(then)i(at)e(least)262 1124 y(one)f(pair)f(among)f Ff(f)p Fd(v)598 1130 y Fm(1)616 1124 y Fd(;)7 b(v)655 1130 y Fm(2)674 1124 y Fd(;)g(v)713 1130 y Fm(3)731 1124 y Ff(g)13 b Fn(is)h(also)f(related.)i(W)m(e)e(can)h(call)f(suc)o(h)i(a) f(relation)f Fh(claw-fr)n(e)n(e)262 1174 y Fn(|)g(no)h(no)q(de)g(is)g (related)g(to)g(three)h(no)q(des)g(that)f(are)g(themselv)o(es)g(m)o (utually)d(unrelated.)324 1225 y(In)19 b(tests)h(on)f(the)h(subgraphs)f Fd(H)s Fn(,)g(w)o(e)g(\014nd)g(that)g(a)g(large)f(fraction)h(of)f(all)g (pairs)h(of)262 1275 y(no)q(des)f Fd(u;)7 b(v)18 b Ff(2)f Fd(H)j Fn(are)e(related)g(b)o(y)f(alternating)g(connectivit)o(y)m(.)g (Among)e(pairs)j(that)f(are)262 1325 y(related,)e(w)o(e)g(can)g (de\014ne)h(their)g Fh(undir)n(e)n(cte)n(d)f(distanc)n(e)h Fn(as)f(the)g(length)g(of)g(the)g(shortest)i Fd(u)p Fn(-)262 1375 y Fd(v)f Fn(path)f(in)g Fd(H)481 1381 y Fe(u)502 1375 y Fn(;)g(and)f(w)o(e)i(can)f(de\014ne)h(their)g Fh(alternating)f(distanc)n(e)h Fn(as)f(the)g(length)g(of)g(the)262 1424 y(shortest)d(alternating)e Fd(u)p Fn(-)p Fd(v)i Fn(path)f(in)g Fd(H)s Fn(.)f(W)m(e)h(\014nd)g(that)g(the)g(a)o(v)o (erage)g(alternating)g(distance)262 1474 y(b)q(et)o(w)o(een)j(related)f (pairs)g(is)f(generally)g(at)h(most)e(a)i(factor)g(of)f(t)o(w)o(o)g (more)f(than)i(the)g(a)o(v)o(erage)262 1524 y(undirected)h(distance)h (b)q(et)o(w)o(een)f(them;)f(this)g(indicates)h(that)f(the)h (biconnected)h(n)o(uclei)f Fd(H)262 1574 y Fn(are)g(ric)o(h)g(in)f (short,)h(alternating)f(paths.)262 1714 y Fi(4)56 b(Mo)r(del)262 1822 y Fn(In)20 b(this)h(section)h(w)o(e)f(la)o(y)e(the)j(foundation)d (for)i(a)f(class)h(of)f(plausible)g(random)g(graph)262 1872 y(mo)q(dels)14 b(in)i(whic)o(h)g(w)o(e)g(can)g(hop)q(e)g(to)g (establish)g(man)o(y)f(of)g(our)h(observ)n(ations)g(ab)q(out)g(the)262 1921 y(lo)q(cal)c(structure)k(of)e(the)g(W)m(eb)g(graph.)f(There)i(are) f(a)f(n)o(um)o(b)q(er)h(of)f(reasons)i(for)e(dev)o(eloping)262 1971 y(suc)o(h)h(a)g(mo)q(del:)279 2061 y(1.)20 b(It)12 b(allo)o(ws)e(us)j(to)e(mo)q(del)f(v)n(arious)h(structural)i(prop)q (erties)g(of)e(the)i(W)m(eb)e(graph)h(|)f(no)q(de)332 2110 y(degrees,)22 b(neigh)o(b)q(orho)q(o)q(d)e(structures,)i(etc.)f (Of)g(particular)f(in)o(terest)h(to)g(us)g(is)f(the)332 2160 y(distribution)d(of)g(W)m(eb)g(structures)j(suc)o(h)f(as)e Fd(C)1091 2166 y Fe(i;j)1130 2160 y Fn('s)g(whic)o(h)h(are)g (signatures)g(of)f(W)m(eb)332 2210 y(comm)o(unities)11 b(or)j(other)h(W)m(eb)e(phenomena)g(of)h(in)o(terest.)279 2261 y(2.)20 b(It)c(allo)o(ws)f(us)h(to)g(predict)g(the)h(b)q(eha)o (vior)f(of)f(algorithms)e(on)j(the)h(W)m(eb;)e(this)h(is)f(is)h(of)332 2311 y(particular)e(in)o(terest)h(when)g(these)g(algorithms)d(are)j(do) q(omed)e(to)h(p)q(erform)f(p)q(o)q(orly)h(on)332 2361 y(w)o(orst-case)h(graphs.)279 2412 y(3.)20 b(It)d(suggests)i (structural)f(prop)q(erties)g(of)f(to)q(da)o(y's)g(W)m(eb)f(that)i(w)o (e)f(migh)o(t)e(b)q(e)j(able)f(to)332 2462 y(v)o(erify)d(and)f(then)i (exploit.)p eop %%Page: 14 14 14 13 bop 279 224 a Fn(4.)20 b(It)c(allo)o(ws)f(us)i(to)f(mak)o(e)f (predictions)i(ab)q(out)f(the)h(shap)q(e)g(of)e(the)i(W)m(eb)f(graph)g (in)g(the)332 274 y(future.)262 370 y Fh(Desider)n(ata)h(for)g(a)h(Web) h(gr)n(aph)e(mo)n(del.)25 b Fn(W)m(e)16 b(b)q(egin)h(b)o(y)g(reviewing) g(some)f(criteria)h(that)262 420 y(are)e(desirable)g(in)g(suc)o(h)h(a)e (graph)h(mo)q(del;)e(man)o(y)g(of)i(these)h(are)g(motiv)n(ated)d(b)o(y) h(empirical)262 470 y(observ)n(ations)k(on)g(the)h(structure)h(of)e (the)h(W)m(eb)e(graph.)h(Next)h(w)o(e)f(presen)o(t)i(our)e(mo)q(del.) 262 519 y(Note)f(that)h(w)o(e)f(do)h(not)f(seek)h(to)g(mo)q(del)e(the)h (text)h(or)g(the)g(sizes)g(of)f(the)h(pages;)f(w)o(e)h(are)262 569 y(only)13 b(in)o(terested)j(here)g(in)e(the)h(in)o(terconnection)g (patterns)g(of)f(links)g(b)q(et)o(w)o(een)i(pages.)e(W)m(e)262 619 y(w)o(ould)f(lik)o(e)g(our)h(mo)q(del)e(to)i(ha)o(v)o(e)f(the)i (follo)o(wing)c(features:)279 697 y(1.)20 b(It)14 b(should)g(ha)o(v)o (e)f(a)h(succinct)h(and)f(fairly)f(natural)g(description.)279 746 y(2.)20 b(It)f(should)g(b)q(e)g(ro)q(oted)g(in)g(a)f(plausible)g (macro-lev)o(el)f(pro)q(cess)k(for)d(the)i(creation)f(of)332 796 y(con)o(ten)o(t)c(on)f(the)g(W)m(eb.)g(W)m(e)f(cannot)i(hop)q(e)f (to)g(mo)q(del)f(the)h(detailed)g(b)q(eha)o(vior)g(of)g(the)332 846 y(man)o(y)c(users)j(creating)f(W)m(eb)g(con)o(ten)o(t.)g(Instead,)g (w)o(e)g(only)f(desire)i(that)f(the)g(aggregate)332 896 y(formation)7 b(of)j(W)m(eb)f(structure)j(b)q(e)e(captured)h(w)o(ell)e (b)o(y)h(our)g(graph)f(mo)q(del.)f(Th)o(us,)i(while)332 945 y(the)15 b(mo)q(del)e(is)h(describ)q(ed)i(as)f(a)f(sto)q(c)o (hastic)h(pro)q(cess)h(for)e(the)h(creation)g(of)e(individual)332 995 y(pages,)e(w)o(e)h(are)g(really)f(only)f(concerned)k(with)d(the)h (aggregate)f(consequences)j(of)d(these)332 1045 y(individual)h (actions.)279 1094 y(3.)20 b(It)13 b(should)f(not)g(require)h(some)f Fh(a)i(priori)h Fn(static)e(set)g(of)f(\\topics")g(that)h(are)f(part)h (of)f(the)332 1144 y(mo)q(del)18 b(description)i(|)e(the)i(ev)o (olution)e(of)h(in)o(teresting)h(topics)f(and)g(comm)o(unities)332 1194 y(should)h(instead)g(b)q(e)g(an)g(emergen)o(t)g(feature)h(of)e (the)h(mo)q(del.)1329 1179 y Fm(1)1366 1194 y Fn(Suc)o(h)g(a)g(mo)q (del)e(has)332 1243 y(sev)o(eral)c(adv)n(an)o(tages:)358 1291 y Fg({)21 b Fn(It)e(is)g(extremely)g(di\016cult)f(to)h(c)o (haracterize)i(the)f(set)g(of)f(topics)g(on)g(the)h(W)m(eb;)403 1341 y(th)o(us)e(it)f(w)o(ould)g(b)q(e)h(useful)g(to)f(dra)o(w)h (statistical)f(conclusions)h(without)f(suc)o(h)i(a)403 1391 y(c)o(haracterization.)358 1440 y Fg({)i Fn(The)c(set)h(of)f (topics)g(re\015ected)i(in)e(W)m(eb)g(con)o(ten)o(t)h(has)f(pro)o(v)o (en)g(to)g(b)q(e)h(fairly)e(dy-)403 1490 y(namic.)c(Th)o(us,)i(the)h (shifting)f(landscap)q(e)h(of)e(actual)i(topics)f(will)f(need)j(to)e(b) q(e)h(ad-)403 1539 y(dressed)h(in)d(an)o(y)g(topic-a)o(w)o(are)h(mo)q (del)e(of)i(time-dep)q(enden)o(t)g(gro)o(wth.)279 1587 y(4.)20 b(W)m(e)d(w)o(ould)g(lik)o(e)f(the)i(mo)q(del)e(to)h(re\015ect) i(man)o(y)d(of)g(the)i(structural)h(phenomena)d(w)o(e)332 1637 y(ha)o(v)o(e)e(observ)o(ed)h(in)e(the)i(W)m(eb)e(graph.)262 1758 y Fg(4.1)47 b(A)16 b(class)g(of)f(random)f(graph)h(mo)q(dels)262 1837 y Fn(In)e(our)h(mo)q(del,)e(w)o(e)i(seek)h(to)f(capture)h(the)g (follo)o(wing)c(in)o(tuition:)287 1916 y Fg({)21 b Fn(some)15 b(page)h(creators)h(on)e(to)q(da)o(y's)g(W)m(eb)h(ma)o(y)d(link)i(to)h (other)g(sites)h(without)e(regard)332 1966 y(to)f(the)g(topics)g(that)g (are)h(already)e(represen)o(ted)k(on)d(the)g(W)m(eb,)f(but)287 2014 y Fg({)21 b Fh(most)f Fn(page)c(creators)h(will)d(b)q(e)j(dra)o (wn)e(to)h(W)m(eb)g(pages)g(co)o(v)o(ering)f(existing)h(topics)g(of)332 2064 y(in)o(terest)e(to)f(them,)f(and)h(will)f(link)g(to)h(pages)g (within)g(some)f(of)g(these)j(existing)e(topics.)324 2144 y(W)m(e)18 b(ha)o(v)o(e)h(already)g(observ)o(ed)h(that)f(the)h(W)m (eb)f(graph)g(has)g(man)o(y)e(h)o(ub)i(pages)g(that)262 2193 y(con)o(tain)13 b(resource)j(lists)e(fo)q(cused)h(on)f(a)g(topic.) g(Here)h(is)f(the)h(dominan)o(t)c(phenomenon)j(for)262 2243 y(link-creation)c(in)h(our)g(mo)q(del:)e(a)i(user)i(encoun)o(ters) g(a)e(resource)i(list)e(for)g(a)f(topic)i(of)e(in)o(terest)262 2293 y(to)j(him,)f(and)i(includes)g(man)o(y)e(links)h(from)f(this)i (list)g(in)f(his/her)h(page.)p 262 2328 237 2 v 270 2355 a Fl(1)300 2371 y Fk(In)f(particular,)h(w)o(e)f(a)o(v)o(oid)h(mo)q (dels)g(of)f(the)f(form)h(\\Assume)g(eac)o(h)h(no)q(de)f(is)h(some)f (com)o(bination)300 2417 y(of)g(topics,)g(and)h(add)f(an)h(edge)f(from) g(one)g(page)g(to)g(another)h(with)f(probabili)q(t)o(y)i(dep)q(enden)o (t)g(on)300 2462 y(some)e(function)i(of)d(their)i(resp)q(ectiv)o(e)h (com)o(binations.")p eop %%Page: 15 15 15 14 bop 324 224 a Fn(W)m(e)11 b(reiterate)h(that)f(this)h(pro)q(cess) h(is)e Fh(not)k Fn(mean)o(t)10 b(to)h(re\015ect)i(individual)c(user)k (b)q(eha)o(vior)262 274 y(on)18 b(the)i(W)m(eb;)e(rather,)h(it)g(is)f (a)h(lo)q(cal)f(pro)q(cedure)j(whic)o(h)d(in)h(aggregate)g(w)o(orks)g (w)o(ell)f(in)262 324 y(describing)11 b(page)f(creation)h(on)g(the)g(W) m(eb)f(and)h(whic)o(h)f(implicitly)d(captures)13 b(topic)d(creation)262 374 y(as)16 b(follo)o(ws:)e(\014rst,)j(a)f(few)h(scattered)h(pages)f(b) q(egin)f(to)g(app)q(ear)h(ab)q(out)g(the)g(topic.)e(Then,)262 423 y(as)20 b(users)h(in)o(terested)h(in)e(the)h(topic)f(reac)o(h)g (critical)g(mass,)f(they)h(b)q(egin)h(linking)d(these)262 473 y(scattered)j(pages)e(together,)h(and)f(other)g(in)o(terested)i (users)g(are)e(able)g(to)g(disco)o(v)o(er)h(and)262 523 y(link)c(to)i(the)g(topic)f(more)g(easily)m(.)f(This)i(creates)h(a)f (\\lo)q(cally)e(dense")j(subgraph)f(around)262 573 y(the)f(topic)f(of)g (in)o(terest.)h(This)g(in)o(tuitiv)o(e)f(view)g(summarizes)f(the)i(pro) q(cess)h(from)d(a)i(page-)262 623 y(creator's)12 b(standp)q(oin)o(t;)g (w)o(e)g(no)o(w)g(recast)h(this)f(form)o(ulation)d(in)j(terms)g(of)f(a) h(random)f(graph)262 672 y(mo)q(del)h(that)i(|)f(again,)f(on)i (aggregate)g(|)f(captures)j(the)e(ab)q(o)o(v)o(e)g(in)o(tuition.)324 730 y(Indeed,)g(it)f(is)h(our)f(thesis)i(that)e(random)f(cop)o(ying)h (is)h(a)f(simple,)f(plausible)g(sto)q(c)o(hastic)262 780 y(mec)o(hanism)h(for)i(creating)h(Zip\014an)g(degree)h (distributions.)e(Belo)o(w,)g(w)o(e)h(state)g(at)g(a)f(high)262 830 y(lev)o(el)g(our)i(mo)q(del)d(for)i(the)h(ev)o(olution)e(of)h(the)h (W)m(eb)e(graph.)h(W)m(e)g(are)g(unable)h(to)f(pro)o(vide)262 879 y(complete)i(probabilistic)g(analyses)h(of)f(the)i(graphs)f (generated)h(b)o(y)f(ev)o(en)h(the)f(simplest)262 929 y(concrete)j(instan)o(tiations)e(of)g(suc)o(h)h(mo)q(dels.)e(Heuristic) i(calculations,)f(ho)o(w)o(ev)o(er,)g(yield)262 979 y(distributions)11 b(for)g(degree)i(sequences,)h Fd(C)918 985 y Fe(i;j)956 979 y Fn('s)e(and)f(other)h(lo)q(cal)f(structures)j(that)e(conform)262 1029 y(remark)n(ably)g(w)o(ell)h(with)g(our)h(observ)n(ations.)324 1086 y(Our)e(mo)q(del)f(is)h(c)o(haracterized)i(b)o(y)d(four)h(sto)q(c) o(hastic)h(pro)q(cesses)i(|)c Fh(cr)n(e)n(ation)h Fn(pro)q(cesses)262 1136 y Ff(C)284 1142 y Fe(v)313 1136 y Fn(and)d Ff(C)411 1142 y Fe(e)438 1136 y Fn(for)g(no)q(de-)h(and)f(edge-creation,)h(and)g Fh(deletion)f Fn(pro)q(cesses)j Ff(D)1378 1142 y Fe(v)1407 1136 y Fn(and)e Ff(D)1516 1142 y Fe(e)1543 1136 y Fn(for)f(no)q(de-)262 1186 y(and)15 b(edge-deletion.)g(These)i(pro)q(cesses)h(are)e (discrete-time)g(pro)q(cesses.)h(Eac)o(h)f(pro)q(cess)i(is)262 1236 y(a)13 b(function)h(of)f(the)h(time)f(step,)h(and)g(of)f(the)i (curren)o(t)g(graph.)324 1293 y(A)10 b(simple)f(no)q(de-creation)i(pro) q(cess)h(w)o(ould)e(b)q(e)h(the)g(follo)o(wing:)c(indep)q(enden)o(tly) 12 b(at)e(eac)o(h)262 1343 y(step,)18 b(create)h(a)f(no)q(de)g(with)f (probabilit)o(y)f Fd(\013)975 1349 y Fe(c)992 1343 y Fn(\()p Fd(t)p Fn(\).)h(W)m(e)h(could)f(ha)o(v)o(e)h(a)g(similar)d (Bernoulli)262 1393 y(mo)q(del)g(with)h(probabilit)o(y)f Fd(\013)727 1399 y Fe(d)746 1393 y Fn(\()p Fd(t)p Fn(\))i(for)f(no)q (de)h(deletion;)f(up)q(on)h(deleting)f(a)h(no)q(de,)f(w)o(e)h(also)262 1443 y(delete)d(all)e(its)h(inciden)o(t)g(edges.)h(Clearly)f(w)o(e)g (could)g(tailor)g(these)h(probabilities)f(to)g(re\015ect)262 1493 y(the)h(gro)o(wth)g(rates)g(of)g(the)g(W)m(eb,)f(the)i(half-life)d (of)h(pages,)h(etc.)324 1550 y(The)20 b(edge)g(pro)q(cesses)i(are)e (rather)g(more)f(in)o(teresting.)g(W)m(e)g(b)q(egin)h(with)f(the)h (edge-)262 1600 y(creation)14 b(pro)q(cess)i Ff(C)588 1606 y Fe(e)605 1600 y Fn(.)e(A)o(t)g(eac)o(h)g(step)h(w)o(e)f(sample)f (a)h(probabilit)o(y)e(distribution)h(to)h(deter-)262 1650 y(mine)d(a)i(no)q(de)h Fd(v)h Fn(to)e(add)g(edges)h(out)f(of,)f (and)h(a)g(n)o(um)o(b)q(er)g(of)f(edges)j Fd(k)f Fn(that)f(will)f(b)q (e)i(added.)262 1700 y(With)h(probabilit)o(y)f Fd(\014)k Fn(w)o(e)e(add)f Fd(k)i Fn(edges)f(from)e Fd(v)k Fn(to)d(no)q(des)i(c)o (hosen)f(indep)q(enden)o(tly)h(and)262 1749 y(uniformly)10 b(at)j(random.)e(With)i(probabilit)o(y)e(1)d Ff(\000)g Fd(\014)r Fn(,)13 b(w)o(e)g Fh(c)n(opy)h Fd(k)g Fn(edges)g(from)e(a)h (randomly)262 1799 y(c)o(hosen)18 b(no)q(de)g(to)f Fd(v)q Fn(.)g(By)h(this)f(w)o(e)h(mean)e(that)h(w)o(e)h(c)o(ho)q(ose)g(a)f(no) q(de)h Fd(u)f Fn(at)g(random,)f(and)262 1849 y(create)c(edges)g(from)d Fd(v)j Fn(to)f(no)q(des)h Fd(w)f Fn(suc)o(h)h(that)f(\()p Fd(u;)c(w)q Fn(\))j(is)h(an)f(edge.)h(One)h(migh)o(t)d(reasonably)262 1899 y(exp)q(ect)16 b(that)g(m)o(uc)o(h)e(of)g(the)i(time,)e Fd(u)h Fn(will)f(not)h(ha)o(v)o(e)g(out-degree)h(exactly)g Fd(k)q Fn(;)e(if)h(the)h(out-)262 1949 y(degree)d(of)e Fd(u)h Fn(exceeds)h Fd(k)g Fn(w)o(e)f(pic)o(k)g(a)f(random)g(subset)i (of)e(size)i Fd(k)q Fn(.)e(If)h(on)f(the)i(other)f(hand)g(the)262 1998 y(out-degree)i(of)e Fd(u)h Fn(is)f(less)i(than)f Fd(k)h Fn(w)o(e)f(\014rst)h(cop)o(y)f(the)g(edges)h(out)f(of)f Fd(u)p Fn(,)h(then)g(pic)o(k)g(another)262 2048 y(random)i(no)q(de)j Fd(u)545 2033 y Fb(0)574 2048 y Fn(to)f(cop)o(y)g(from,)e(and)i(so)h (on)f(un)o(til)f(w)o(e)i(ha)o(v)o(e)f(enough)g(edges.)h(Suc)o(h)g(a)262 2098 y(cop)o(ying)d(pro)q(cess)j(is)e(not)g(unnatural,)g(and)g (consisten)o(t)h(with)f(the)h(qualitativ)o(e)e(in)o(tuition)262 2148 y(at)e(the)i(b)q(eginning)e(of)g(this)h(section.)324 2205 y(A)19 b(simple)g(edge-deletion)h(pro)q(cess)h Ff(D)949 2211 y Fe(e)987 2205 y Fn(w)o(ould)d(again)h(b)q(e)h(a)f(Bernoulli)g (pro)q(cess)j(in)262 2255 y(whic)o(h)14 b(at)g(eac)o(h)h(step,)h(with)e (probabilit)o(y)f Fd(\016)r Fn(,)h(w)o(e)h(delete)g(a)f(randomly)f(c)o (hosen)i(no)q(de.)g(The)262 2305 y(probabilit)o(y)f(that)i(a)f (particular)h(no)q(de)g Fd(v)h Fn(is)f(deleted)h(w)o(ould)e(ideally)f (b)q(e)j(non-increasing)262 2355 y(in)c(its)h(in-degree.)324 2412 y(W)m(e)h(illustrate)g(these)i(ideas)f(with)f(a)g(v)o(ery)h (simple)e(sp)q(ecial)i(case.)g(Consider)g(a)f(mo)q(del)262 2462 y(in)i(whic)o(h)h(a)f(no)q(de)h(is)g(created)h(at)f(ev)o(ery)g (step.)h(No)q(des)f(and)g(edges)h(are)f(nev)o(er)h(deleted,)p eop %%Page: 16 16 16 15 bop 262 224 a Fn(so)17 b(the)h(graph)f(k)o(eeps)h(on)f(gro)o (wing.)f(Consider)h(the)h(follo)o(wing)d(edge)j(pro)q(cess:)g(for)f (some)262 274 y Fd(\014)d Ff(2)d Fn(\(0)p Fd(;)c Fn(1\),)i(at)i(eac)o (h)g(step)g(the)g(newly-created)h(no)q(de)f(p)q(oin)o(ts)g(to)f(a)h(no) q(de)g(c)o(hosen)g(uniformly)262 324 y(at)16 b(random.)f(With)h (probabilit)o(y)f(1)c Ff(\000)g Fd(\014)r Fn(,)17 b(it)g(copies)g(a)g (uniform)d(random)h(edge)j(out)f(of)f(a)262 374 y(random)e(no)q(de.)j (Sim)o(ulations)d(\(and)i(heuristic)h(calculations\))f(suggest)i(that)e (under)h(this)262 423 y(mo)q(del,)8 b(the)k(probabilit)o(y)d(that)h(a)h (no)q(de)g(has)g(in-degree)g Fd(i)g Fn(con)o(v)o(erges)h(to)e Fd(i)1400 408 y Fb(\000)p Fm(1)p Fe(=)p Fm(\(1)p Fb(\000)p Fe(\014)q Fm(\))1551 423 y Fn(.)g(Similar)262 473 y(calculations)j (suggest)i(that)g(the)g(n)o(um)o(b)q(ers)f(of)f(cores)j Fd(C)1147 479 y Fe(i;j)1200 473 y Fn(are)f(signi\014can)o(tly)e(larger) h(than)262 523 y(random)d(graphs)h(in)g(whic)o(h)h(edges)g(go)f(to)h (uniform,)d(indep)q(enden)o(t)k(random)d(destinations.)324 574 y(Clearly)20 b(the)h(pro)q(cesses)i(creating)e(these)h(graphs,)f (as)f(w)o(ell)g(as)h(the)g(statistics)h(and)262 624 y(structures)17 b(observ)o(ed,)f(di\013er)f(signi\014can)o(tly)f(from)f(those)j(of)f (traditional)e(random)h(graph)262 674 y(mo)q(dels.)9 b(This)i(is)g(b)q(oth)g(a)f(feature)i(and)f(a)g(c)o(hallenge.)f(On)h (the)h(one)f(hand,)f(the)i(relationship)262 723 y(b)q(et)o(w)o(een)j (cop)o(ying)d(and)i(Zip\014an)f(distributions)h(is)f(of)g(in)o(trinsic) h(in)o(terest)g(for)g(a)f(v)n(ariet)o(y)g(of)262 773 y(reasons)18 b(\(giv)o(en)f(suc)o(h)h(distributions)g(also)e(arise)i (in)f(a)g(n)o(um)o(b)q(er)g(of)g(settings)h(outside)g(of)262 823 y(the)f(W)m(eb)f(|)g(in)g(term)g(frequencies,)i(in)e(the)h(genome,) f(etc.\).)g(On)h(the)h(other)f(hand,)f(the)262 873 y(pro)q(cess)e(of)e (cop)o(ying)g(also)g(generates)j(a)d(m)o(yriad)f(of)h(dep)q(endencies)j (b)q(et)o(w)o(een)g(the)e(random)262 923 y(v)n(ariables)e(of)h(in)o (terest,)i(so)e(that)h(the)g(study)g(of)f(suc)o(h)h(graphs)g(calls)f (for)g(a)h(whole)f(new)h(suite)262 972 y(of)g(analytical)f(to)q(ols.) 262 1111 y Fi(5)56 b(Conclusion)262 1216 y Fn(Our)14 b(w)o(ork)g(raises)g(a)g(n)o(um)o(b)q(er)f(of)g(areas)i(for)e(further)i (w)o(ork:)279 1304 y(1.)20 b(Ho)o(w)11 b(can)h(w)o(e)f(annotate)h(and)f (organize)g(the)h(comm)o(unities)d(disco)o(v)o(ered)j(b)o(y)f(the)h (tra)o(wl-)332 1353 y(ing)h(pro)q(cess)j(of)d(Section)i(2.2?)279 1404 y(2.)20 b(What)10 b(extensions)g(and)g(applications)f(can)h(b)q(e) h(found)e(for)h(the)g(connectivit)o(y)g(measures)332 1454 y(discussed)16 b(in)d(Section)h(3.3?)279 1505 y(3.)20 b(What)14 b(are)h(the)f(prop)q(erties)i(and)e(ev)o(olution)f(of)h (random)f(graphs)h(generated)i(b)o(y)e(sp)q(e-)332 1555 y(ci\014c)g(v)o(ersions)g(of)f(our)h(mo)q(dels)f(in)g(Section)h(4?)f (This)h(w)o(ould)e(b)q(e)j(the)f(analogue)f(of)g(the)332 1605 y(study)h(of)g(traditional)e(random)g(graph)i(mo)q(dels)f(suc)o(h) i(as)f Ff(G)1279 1611 y Fe(n;p)1328 1605 y Fn(.)279 1656 y(4.)20 b(Ho)o(w)13 b(do)g(w)o(e)h(devise)g(and)f(analyze)h(algorithms) d(that)i(are)h(e\016cien)o(t)g(on)f(suc)o(h)i(graphs?)332 1705 y(Again,)e(this)h(study)g(has)g(an)g(analogue)f(with)g (traditional)g(random)f(graph)i(mo)q(dels.)279 1756 y(5.)20 b(What)g(can)g(w)o(e)h(infer)f(ab)q(out)g(the)g(distributed)h(so)q (ciological)e(pro)q(cess)j(of)d(creating)332 1806 y(con)o(ten)o(t)c(on) e(the)i(W)m(eb?)324 1893 y(W)m(e)f(thank)h(Byron)g(Dom)e(and)h(Ron)g(F) m(agin)g(for)g(their)h(commen)o(ts.)e(The)i(w)o(ork)f(of)g(Jon)262 1942 y(Klein)o(b)q(erg)f(w)o(as)g(supp)q(orted)h(in)e(part)h(b)o(y)g (an)g(Alfred)g(P)m(.)f(Sloan)g(Researc)o(h)i(F)m(ello)o(wship)e(and)262 1992 y(b)o(y)h(NSF)h(F)m(acult)o(y)f(Early)h(Career)h(Dev)o(elopmen)o (t)e(Aw)o(ard)h(CCR-9701399.)262 2131 y Fi(References)262 2232 y Fk(1.)20 b(S.)c(Abiteb)q(oul,)i(D.)e(Quass,)g(J.)f(McHugh,)i(J.) e(Widom,)i(and)g(J.)e(W)m(einer.)i(The)f(Lorel)h(Query)293 2277 y(language)e(for)e(semistructured)i(data.)e Fa(Intl.)f(J.)i(on)f (Digital)f(Libr)n(aries,)f Fk(1\(1\):68-88,)i(1997.)262 2324 y(2.)20 b(R.)e(Agra)o(w)o(al)g(and)g(R.)f(Srik)n(an)o(th.)i(F)m (ast)f(algorithms)i(for)d(mining)j(asso)q(ciation)g(rules.)e Fa(Pr)n(o)n(c.)293 2370 y(VLDB,)12 b Fk(1994.)262 2417 y(3.)20 b(G.)f(O.)f(Aro)q(cena,)h(A.)f(O.)g(Mendelzon,)i(G.)f(A.)f (Mihaila.)j(Applications)h(of)c(a)h(W)m(eb)h(query)293 2462 y(language.)15 b Fa(Pr)n(o)n(c.)e(6th)f(WWW)j(Conf.)p Fk(,)d(1997.)p eop %%Page: 17 17 17 16 bop 262 224 a Fk(4.)20 b(K.)13 b(Bharat)i(and)g(A.)e(Bro)q(der.)i (A)e(tec)o(hnique)j(for)e(measuring)i(the)e(relativ)o(e)h(size)g(and)g (o)o(v)o(erlap)293 270 y(of)e(public)i(W)m(eb)e(searc)o(h)h(engines.)g Fa(Pr)n(o)n(c.)f(7th)g(WWW)i(Conf.,)c Fk(1998.)262 314 y(5.)20 b(K.)d(Bharat)i(and)g(M.)e(R.)h(Henzinger.)h(Impro)o(v)o(ed)g (algorithms)h(for)d(topic)i(distilla)q(tion)j(in)c(a)293 359 y(h)o(yp)q(erlink)o(ed)e(en)o(vironmen)o(t.)f Fa(Pr)n(o)n(c.)e(A)o (CM)h(SIGIR)p Fk(,)d(1998.)262 403 y(6.)20 b(S.)12 b(Brin)h(and)f(L.)g (P)o(age.)g(The)g(anatom)o(y)h(of)e(a)h(large-scale)i(h)o(yp)q (ertextual)g(W)m(eb)f(searc)o(h)f(engine.)293 449 y Fa(Pr)n(o)n(c.)h (7th)g(WWW)h(Conf.)p Fk(,)e(1998.)262 492 y(7.)20 b(B.)13 b(Bollob\023)-19 b(as.)15 b Fa(R)n(andom)d(Gr)n(aphs)p Fk(,)f(Academic)j(Press,)f(1985.)262 536 y(8.)20 b(J.)11 b(Carri)o(\022)-18 b(ere)12 b(and)g(R.)f(Kazman.)h(W)m(ebQuery:)g (Searc)o(hing)i(and)e(visualizi)q(ng)i(the)e(W)m(eb)g(through)293 582 y(connectivit)o(y)m(.)j Fa(Pr)n(o)n(c.)e(6th)g(WWW)h(Conf.)p Fk(,)e(1997.)262 626 y(9.)20 b(S.)11 b(Chakrabarti,)h(B.)f(Dom,)g(D.)g (Gibson,)h(J.)e(Klein)o(b)q(erg,)j(P)m(.)d(Ragha)o(v)n(an)j(and)e(S.)g (Ra)r(jagopalan.)293 671 y(Automatic)f(resource)g(compilation)i(b)o(y)d (analyzing)j(h)o(yp)q(erlink)f(structure)f(and)g(asso)q(ciated)h(text.) 293 717 y Fa(Pr)n(o)n(c.)i(7th)g(WWW)h(Conf.)p Fk(,)e(1998.)262 761 y(10.)20 b(S.)25 b(Chakrabarti,)h(B.)f(Dom,)g(S.)g(R.)f(Kumar,)h(P) m(.)g(Ragha)o(v)n(an,)h(S.)f(Ra)r(jagopalan,)i(and)293 806 y(A.)19 b(T)m(omkins.)g(Exp)q(erimen)o(ts)j(in)e(topic)g (distillati)q(on.)i Fa(SIGIR)c(workshop)g(on)h(hyp)n(ertext)e(IR)p Fk(,)293 852 y(1998.)262 896 y(11.)j(S.)12 b(Chakrabarti)h(and)f(B.)g (Dom)g(and)g(P)m(.)f(Indyk.)h(Enhanced)h(h)o(yp)q(ertext)g (classi\014cation)i(using)293 942 y(h)o(yp)q(erlinks.)h Fa(Pr)n(o)n(c.)d(A)o(CM)h(SIGMOD)p Fk(,)e(1998.)262 985 y(12.)20 b(H.)13 b(T.)f(Da)o(vis.)i Fa(The)f(A)o(nalysis)e(of)i(Ec)n (onomic)f(Time)i(Series.)d Fk(Principia)16 b(press,)d(1941.)262 1029 y(13.)20 b(R.)11 b(Do)o(wney)m(,)f(M.)g(F)m(ello)o(ws.)i(P)o (arametrized)f(Computational)i(F)m(easibili)q(t)o(y)m(.)g(In)d Fa(F)m(e)n(asible)f(Math-)293 1075 y(ematics)j(II)p Fk(,)g(P)m(.)h (Clote)g(and)h(J.)e(Remmel,)h(eds.,)g(Birkhauser,)i(1994.)262 1119 y(14.)20 b(L.)13 b(Egghe,)g(R.)g(Rousseau,)h Fa(Intr)n(o)n (duction)c(to)j(Informetrics)p Fk(,)e(Elsevier,)j(1990.)262 1162 y(15.)20 b(D.)12 b(Florescu,)i(A.)d(Levy)i(and)g(A.)f(Mendelzon.)i (Database)f(tec)o(hniques)i(for)d(the)g(W)m(orld)i(Wide)293 1208 y(W)m(eb:)f(A)g(surv)o(ey)m(.)g Fa(SIGMOD)g(R)n(e)n(c)n(or)n(d)p Fk(,)f(27\(3\):)h(59-74,)g(1998.)262 1252 y(16.)20 b(E.)11 b(Gar\014eld.)h(Citation)h(analysis)g(as)f(a)f(to)q(ol)h(in)f(journal)i (ev)n(aluation.)g Fa(Scienc)n(e)p Fk(,)8 b(178:471{479,)293 1298 y(1972.)262 1341 y(17.)20 b(N.)10 b(Gilb)q(ert.)i(A)e(sim)o (ulation)j(of)e(the)f(structure)h(of)g(academic)g(science.)h Fa(So)n(ciolo)n(gic)n(a)o(l)c(R)n(ese)n(ar)n(ch)293 1387 y(Online)p Fk(,)j(2\(2\),)i(1997.)262 1431 y(18.)20 b(G.)11 b(Golub,)i(C.)d(F.)h(V)m(an)g(Loan.)g Fa(Matrix)h(Computations)p Fk(,)c(Johns)j(Hopkins)i(Univ)o(ersit)o(y)g(Press,)293 1476 y(1989.)262 1520 y(19.)20 b(M.)13 b(R.)g(Henzinger,)h(P)m(.)f (Ragha)o(v)n(an,)h(and)g(S.)e(Ra)r(jagopalan.)k(Computing)e(on)g(data)f (streams.)293 1566 y Fa(AMS-DIMA)o(CS)f(series,)g Fk(sp)q(ecial)j (issue)f(on)f(computing)i(on)e(v)o(ery)h(large)g(datasets,)f(1998.)262 1610 y(20.)20 b(M.)14 b(M.)f(Kessler.)i(Bibliograph)q(ic)i(coupling)f (b)q(et)o(w)o(een)f(scien)o(ti\014c)h(pap)q(ers.)e Fa(A)o(meric)n(an)f (Do)n(cu-)293 1655 y(mentation)p Fk(,)d(14:10{25,)k(1963.)262 1699 y(21.)20 b(J.)12 b(Klein)o(b)q(erg.)j(Authoritativ)o(e)g(sources)f (in)f(a)g(h)o(yp)q(erlink)o(ed)j(en)o(vironmen)o(t,)e Fa(J.)g(of)f(the)f(A)o(CM)p Fk(,)293 1745 y(1999,)h(to)g(app)q(ear.)h (Also)f(app)q(ears)h(as)f(IBM)g(Researc)o(h)h(Rep)q(ort)f(RJ)g (10076\(91892\))i(Ma)o(y)e(1997.)262 1789 y(22.)20 b(D.)c(Konopnic)o (ki)i(and)e(O.)f(Shm)o(ueli.)i(Information)g(gathering)g(on)f(the)g(W)m (orld)g(Wide)h(W)m(eb:)293 1834 y(the)10 b(W3QL)g(query)h(language)h (and)f(the)f(W3QS)h(system.)f Fa(T)m(r)n(ans.)g(on)h(Datab)n(ase)d (Systems,)g Fk(1998.)262 1878 y(23.)20 b(S.)15 b(R.)h(Kumar,)f(P)m(.)f (Ragha)o(v)n(an,)j(S.)e(Ra)r(jagopalan)j(and)e(A.)f(T)m(omkins.)g(T)m (ra)o(wling)i(emerging)293 1924 y(cyb)q(er-comm)o(unities)f (automatically)m(.)f Fa(Pr)n(o)n(c.)e(8th)g(WWW)i(Conf.)p Fk(,)c(1999.)262 1967 y(24.)20 b(L.)12 b(V.)f(S.)h(Lakshmanan,)h(F.)e (Sadri,)i(and)g(I.)e(N.)g(Subramanian.)j(A)e(declarativ)o(e)i(approac)o (h)f(to)293 2013 y(querying)k(and)f(restructuring)i(the)d(W)m(orld)i (Wide)f(W)m(eb.)g Fa(Post-ICDE)f(Workshop)f(on)h(RIDE)p Fk(,)293 2059 y(1996.)262 2103 y(25.)20 b(R.)14 b(Larson.)h (Bibliometrics)i(of)d(the)g(W)m(orld)i(Wide)f(W)m(eb:)g(An)f (exploratory)i(analysis)g(of)e(the)293 2148 y(in)o(tellectual)19 b(structure)d(of)f(cyb)q(erspace.)h Fa(A)o(nn.)f(Me)n(eting)f(of)h(the) g(A)o(meric)n(an)f(So)n(c.)h(Info.)f(Sci.)p Fk(,)293 2194 y(1996.)262 2238 y(26.)20 b(A.)13 b(J.)g(Lotk)n(a.)g(The)g (frequency)i(distribution)i(of)c(scien)o(ti\014c)i(pro)q(ductivit)o(y)m (.)h Fa(J.)e(of)f(the)h(Wash-)293 2283 y(ington)e(A)n(c)n(ad.)f(of)j (Sci.)p Fk(,)d(16:317,)i(1926.)262 2327 y(27.)20 b(A.)d(Mendelzon,)j (G.)d(Mihaila,)j(and)e(T.)f(Milo.)i(Querying)g(the)f(W)m(orld)h(Wide)g (W)m(eb,)f Fa(J.)g(of)293 2373 y(Digital)12 b(Libr)n(aries)f Fk(1\(1\):68{88,)j(1997.)262 2417 y(28.)20 b(A.)e(Mendelzon)i(and)f(P)m (.)f(W)m(o)q(o)q(d.)h(Finding)i(regular)f(simple)g(paths)f(in)g(graph)g (databases.)293 2462 y Fa(SIAM)13 b(J.)h(Comp.)p Fk(,)e (24\(6\):1235-1258,)i(1995.)p eop %%Page: 18 18 18 17 bop 262 224 a Fk(29.)20 b(E.)12 b(Sp)q(ertus.)h(P)o(araSite:)g (Mining)h(structural)f(information)h(on)f(the)f(W)m(eb.)g Fa(Pr)n(o)n(c.)g(6th)g(WWW)293 270 y(Conf.)p Fk(,)g(1997.)262 315 y(30.)20 b(D.)i(Tsur,)f(J.)f(Ullman,)j(S.)e(Abiteb)q(oul,)i(C.)e (Clifton,)h(R.)f(Mot)o(w)o(ani,)h(S.)f(Nestoro)o(v,)h(and)293 361 y(A.)11 b(Rosen)o(thal.)j(Query)e(Flo)q(c)o(ks:)h(A)e (generalization)16 b(of)11 b(asso)q(ciation)k(rule)e(mining.)g Fa(Pr)n(o)n(c.)f(A)o(CM)293 407 y(SIGMOD)p Fk(,)g(1998.)262 452 y(31.)20 b(G.)15 b(K.)f(Zipf.)h(Human)g(b)q(eha)o(vior)h(and)g(the) f(principle)i(of)e(least)g(e\013ort.)g Fa(New)g(Y)m(ork:)f(Hafner)p Fk(,)293 498 y(1949.)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF