Biased Random Search in Complex Networks (original) (raw)
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We study random walks on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs of nodes, for a random walk with a memory of one step. We have analyzed one particular model of random walk, where the transition probabilities depend on the number of paths to the second neighbors. The numerical experiments on paradigmatic complex networks verify the validity of the theoretical expressions, and also indicate that the flattening of the stationary occupation probability accompanies a nearly optimal random search.
Searching method through biased random walks on complex networks
Physical Review E, 2009
Information search is closely related to the first-passage property of diffusing particle. The physical properties of diffusing particle is affected by the topological structure of the underlying network. Thus, the interplay between dynamical process and network topology is important to study information search on complex networks. Designing an efficient method has been one of main interests in information search. Both reducing the network traffic and decreasing the searching time have been two essential factors for designing efficient method. Here we propose an efficient method based on biased random walks. Numerical simulations show that the average searching time of the suggested model is more efficient than other well-known models. For a practical interest, we demonstrate how the suggested model can be applied to the peer-to-peer system.
Navigation by anomalous random walks on complex networks
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Anomalous random walks having long-range jumps are a critical branch of dynamical processes on networks, which can model a number of search and transport processes. However, traditional measurements based on mean first passage time are not useful as they fail to characterize the cost associated with each jump. Here we introduce a new concept of mean first traverse distance (MFTD) to characterize anomalous random walks that represents the expected traverse distance taken by walkers searching from source node to target node, and we provide a procedure for calculating the MFTD between two nodes. We use Lévy walks on networks as an example, and demonstrate that the proposed approach can unravel the interplay between diffusion dynamics of Lévy walks and the underlying network structure. Moreover, applying our framework to the famous PageRank search, we show how to inform the optimality of the PageRank search. The framework for analyzing anomalous random walks on complex networks offers a useful new paradigm to understand the dynamics of anomalous diffusion processes, and provides a unified scheme to characterize search and transport processes on networks.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2015
We study the problem of a particle or message that travels as a biased random walk towards a target node in a network in the presence of traps. The bias is represented as the probability p of the particle to travel along the shortest path to the target node. The efficiency of the transmission process is expressed through the fraction f(g) of particles that succeed to reach the target without being trapped. By relating f(g) with the number S of nodes visited before reaching the target, we first show that, for the unbiased random walk, f(g) is inversely proportional to both the concentration c of traps and the size N of the network. For the case of biased walks, a simple approximation of S provides an analytical solution that describes well the behavior of f(g), especially for p>0.5. Also, it is shown that for a given value of the bias p, when the concentration of traps is less than a threshold value equal to the inverse of the mean first passage time (MFPT) between two randomly ch...
All-time dynamics of continuous-time random walks on complex networks
The Journal of Chemical Physics, 2013
The concept of continuous-time random walks (CTRW) is a generalization of ordinary random walk models, and it is a powerful tool for investigating a broad spectrum of phenomena in natural, engineering, social and economic sciences. Recently, several theoretical approaches have been developed that allowed to analyze explicitly dynamics of CTRW at all times, which is critically important for understanding mechanisms of underlying phenomena. However, theoretical analysis has been done mostly for systems with a simple geometry. Here we extend the original method based on generalized master equations to analyze all-time dynamics of CTRW models on complex networks. Specific calculations are performed for models on lattices with branches and for models on coupled parallel-chain lattices. Exact expressions for velocities and dispersions are obtained. Generalized fluctuations theorems for CTRW models on complex networks are discussed.
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Physical Review E, 2005
In many complex systems, for the activity fi of the constituents or nodes i a power-law relationship was discovered between the standard deviation σi and the average strength of the activity: σi ∝ fi α ; universal values α = 1/2 or 1 were found, however, with exceptions. With the help of an impact variable we introduce a random walk model where the activity is the product of the number of visitors at a node and their impact. If the impact depends strongly on the node connectivity and the properties of the carrying network are broadly distributed (like in a scale free network) we find both analytically and numerically non-universal α values. The exponent always crosses over to the universal value of 1 if the external drive dominates.
Exploring Complex Graphs by Random Walks
AIP Conference Proceedings, 2003
We present an algorithm [1] to grow a graph with scale-free structure of in-and out-links and variable wiring diagram in the class of the worldwide Web. We then explore the graph by intentional random walks using local next-near-neighbor search algorithm to navigate through the graph. The topological properties such as betweenness are determined by an ensemble of independent walkers and efficiency of the search is compared on three different graph topologies. In addition we simulate interacting random walks which are created by given rate and navigated in parallel, representing transport with queueing of information packets on the graph.
Random-walk access times on partially disordered complex networks: An effective medium theory
Physical Review E, 2008
An analytic effective medium theory is constructed to study the mean access times for random walks on hybrid disordered structures formed by embedding complex networks into regular lattices, considering transition rates F that are different for steps across lattice bonds from the rates f across network shortcuts. The theory is developed for structures with arbitrary shortcut distributions and applied to a class of partially-disordered traversal enhanced networks in which shortcuts of fixed length are distributed randomly with finite probability. Numerical simulations are found to be in excellent agreement with predictions of the effective medium theory on all aspects addressed by the latter. Access times for random walks on these partially disordered structures are compared to those on small-world networks, which on average appear to provide the most effective means of decreasing access times uniformly across the network.
Random Walks and Search in Time-Varying Networks
Physical Review Letters, 2012
The random walk process underlies the description of a large number of real-world phenomena. Here we provide the study of random walk processes in time-varying networks in the regime of time-scale mixing, i.e., when the network connectivity pattern and the random walk process dynamics are unfolding on the same time scale. We consider a model for time-varying networks created from the activity potential of the nodes and derive solutions of the asymptotic behavior of random walks and the mean first passage time in undirected and directed networks. Our findings show striking differences with respect to the well-known results obtained in quenched and annealed networks, emphasizing the effects of dynamical connectivity patterns in the definition of proper strategies for search, retrieval, and diffusion processes in time-varying networks.