Bipartite graphs Research Papers - Academia.edu (original) (raw)

Bipartite graphs are common in many complex systems as they describe a relationship between two different kinds of actors, e.g., genes and proteins, metabolites and enzymes, authors and articles, or products and consumers. A common... more

Bipartite graphs are common in many complex systems as they describe a relationship between two different kinds of actors, e.g., genes and proteins, metabolites and enzymes, authors and articles, or products and consumers. A common approach to analyze them is to build a graph between the nodes on one side depending on their relationships with nodes on the other side; this so-called one-mode projection is a crucial step for all further analysis but a systematic approach to it was lacking so far. Here, we present a systematic approach that evaluates the significance of the co-occurrence for each pair of nodes v, w, i.e., the number of common neighbors of v and w. It turns out that this can be seen as a special case of evaluating the interestingness of an association rule in data mining. Based on this connection we show that classic interestingness measures in data mining cannot be applied to evaluate most real-world product-consumer relationship data. We thus introduce generalized interestingness measures for both, one-mode projections of bipartite graphs and data mining and show their robustness and stability by example. We also provide theoretical results that show that the old method cannot even be used as an approximative method. In a last step we show that the new interestingness measures show stable and significant results that result in attractive one-mode projections of bipartite graphs.

Abstract. This paper studies competition in a network and how a network structure determines agents' individual payoffs. It constructs a general model of competition that can serve as a reduced form for specific models. The paper shows... more

Abstract. This paper studies competition in a network and how a network structure determines agents' individual payoffs. It constructs a general model of competition that can serve as a reduced form for specific models. The paper shows how agents' outside options, and hence their shares of surplus, derive from “opportunity paths” connecting them to direct and indirect alternative exchanges. Analyzing these paths, results show how third parties' links affect different agents' bargaining power. Even distant links may have large effects on agents' earnings. These payoff results, and the identification of the paths themselves, should prove useful to further analysis of network structure.

In [1] Abdel-Aal has introduced the notions of m-shadow graphs and n-splitting graphs, for all 1 , ≥ n m. In this paper, we prove that, the m-shadow graphs for paths and complete bipartite graphs are odd harmonious graphs for all 1 ≥ m.... more

In [1] Abdel-Aal has introduced the notions of m-shadow graphs and n-splitting graphs, for all 1 , ≥ n m. In this paper, we prove that, the m-shadow graphs for paths and complete bipartite graphs are odd harmonious graphs for all 1 ≥ m. Also, we prove the n-splitting graphs for paths, stars and symmetric product between paths and null graphs are odd harmonious graphs for all 1 ≥ n. In addition, we present some examples to illustrate the proposed theories. Moreover, we show that some families of graphs admit odd harmonious libeling.

We study the problem of computing similarity rankings in large-scale multi-categorical bipartite graphs, where the two sides of the graph represent actors and items, and the items are partitioned into an arbitrary set of categories. The... more

We study the problem of computing similarity rankings in large-scale multi-categorical bipartite graphs, where the two sides of the graph represent actors and items, and the items are partitioned into an arbitrary set of categories. The problem has several real-world applications, including identifying competing advertisers and suggesting related queries in an online advertising system or finding users with similar interests and suggesting content to them. In these settings, we are interested in computing on-the-fly rankings of similar actors, given an actor and an arbitrary subset of categories of interest. Two main challenges arise: First, the bipartite graphs are huge and often lopsided (e.g. the system might receive billions of queries while presenting only millions of advertisers). Second, the sheer number of possible combinations of categories prevents the pre-computation of the results for all of them. We present a novel algorithmic framework that addresses both issues for the computation of several graph-theoretical similarity measures, including # common neighbors, and Personalized PageRank. We show how to tackle the imbalance in the graphs to speed up the computation and provide efficient real-time algorithms for computing rankings for an arbitrary subset of categories. Finally, we show experimentally the accuracy of our approach with real-world data, using both public graphs and a very large dataset from Google AdWords.

This paper presents an algorithm, based on the fixed point iteration, to solve for sizes and biases using transistor compact models such as BSIM3v3, BSIM4, PSP and EKV. The proposed algorithm simplifies the implementation of sizing and... more

This paper presents an algorithm, based on the fixed point iteration, to solve for sizes and biases using transistor compact models such as BSIM3v3, BSIM4, PSP and EKV. The proposed algorithm simplifies the implementation of sizing and biasing operators. Sizing and biasing operators were originally proposed in the hierarchical sizing and biasing methodology. They allow to compute transistors sizes and biases based on transistor compact models while respecting designer's hypotheses. Computed sizes and biases are accurate, and guarantee the correct electrical behavior as expected by the designer. Sizing and biasing operators interface with a Spice-like simulator, allowing possible use of all available compact models for circuit sizing and biasing over different technologies. To illustrate the effectiveness of the proposed algorithm, a folded cascode OTA was efficiently sized with a 130 nm process, then was migrated to a 65 nm technology. Both sizing and migration were performed in...

Bipartite graphs are combinatorial objects bearing some interesting symmetries. Thus, their spectra—eigenvalues of its adjacency matrix—are symmetric about zero, as the corresponding eigenvectors come into pairs. Moreover, vertices in the... more

Bipartite graphs are combinatorial objects bearing some interesting symmetries. Thus, their spectra—eigenvalues of its adjacency matrix—are symmetric about zero, as the corresponding eigenvectors come into pairs. Moreover, vertices in the same (respectively, different) independent set are always at even (respectively, odd) distance. Both properties have well-known consequences in most properties and parameters of such graphs. Roughly speaking, we could say that the conditions for a given property to hold in a general graph can be somehow relaxed to guaranty the same property for a bipartite graph. In this paper we comment upon this phenomenon in the framework of distance-regular graphs for which several characterizations, both of combinatorial or algebraic nature, are known. Thus, the presented characterizations of bipartite distance-regular graphs involve such parameters as the numbers of walks between vertices (entries of the powers of the adjacency matrix A), the crossed local mu...

ABSTRACT Results suggest that there are relations between the decision tree complexity of a Boolean function and its symmetry. A central conjecture is that for any monotone graph property the randomized decision tree complexity does not... more

ABSTRACT Results suggest that there are relations between the decision tree complexity of a Boolean function and its symmetry. A central conjecture is that for any monotone graph property the randomized decision tree complexity does not differ from the deterministic one with more than a constant factor. The authors improve on V. King's Ω( n 5/4) lower bound on the randomized decision tree complexity of monotone graph properties to Ω( n 4/3). The proof follows A. Yao's (1977) approach and improves it in a different direction from King's. At the heart of the proof is a duality argument combined with a new packing lemma for bipartite graphs. Consideration is also given to the question of what distinguishes graph properties from other highly symmetric Boolean functions, where randomization can help significantly. Open questions concerning this problem are discussed

For a bipartite graph G we are able to characterize the complete intersection property of the edge subring in terms of the multiplicity and we give optimal bounds for this number. We give a method to obtain a regular sequence for the... more

For a bipartite graph G we are able to characterize the complete intersection property of the edge subring in terms of the multiplicity and we give optimal bounds for this number. We give a method to obtain a regular sequence for the atomic ideal of G, when G is embedded on an orientable surface. We also give a graph theoretical condition for the edge subring associated with G to be Gorenstein. Finally we give a formula for the multiplicity of edge subrings, of arbitrary simple graphs.

The improvements in disk speeds have not kept up with improvements in processor and memory speeds. Conventional storage techniques, in the face of multimedia data, are inefficient and/or inadequate. Here, an efficient multimedia object... more

The improvements in disk speeds have not kept up with improvements in processor and memory speeds. Conventional storage techniques, in the face of multimedia data, are inefficient and/or inadequate. Here, an efficient multimedia object allocation strategy is presented. We describe a multimedia object model, the object and storage device characteristics, and the fragmentation strategy. A bipartite graph approach is used