Related papers: It's a Small World for Random Surfers

In this report we show that in a planar exponentially growing network consisting of $N$ nodes, congestion scales as $O(N^2/\log(N))$ independently of how flows may be routed. This is in contrast to the $O(N^{3/2})$ scaling of congestion in…

This paper mainly investigates why small-world networks are navigable and how to navigate small-world networks. We find that the navigability can naturally emerge from self-organization in the absence of prior knowledge about underlying…

The understanding of long-distance relations between seismic activities has for long been of interest to seismologists and geologists. In this paper we have used data from the world-wide earthquake catalog for the period between 1972 and…

There has been much recent interest in random graphs sampled uniformly from the n-vertex graphs in a suitable minor-closed class, such as the class of all planar graphs. Here we use combinatorial and probabilistic methods to investigate a…

We considered the Edwards-Wilkinson model on a small-world network. We studied the finite-size behavior of the surface width by performing exact numerical diagonalization for the underlying coupling matrix. We found that the spectrum…

Rank 1 inhomogeneous random graphs are a natural generalization of Erd\H{o}s R\'enyi random graphs. In this generalization each node is given a weight. Then the probability that an edge is present depends on the product of the weights of…

We use the recently introduced small-world networks (SWN) to model cross-linked polymers, as an extension of the linear Rouse-chain. We study the SWN-dynamics under the influence of external forces. Our focus is on the structurally and…

PageRank has numerous applications in information retrieval, reputation systems, machine learning, and graph partitioning. In this paper, we study PageRank in undirected random graphs with an expansion property. The Chung-Lu random graph is…

Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast,…

Random key graphs were introduced to study various properties of the Eschenauer-Gligor key predistribution scheme for wireless sensor networks (WSNs). Recently this class of random graphs has received much attention in contexts as diverse…

We study the random loop model with crosses and bars on sparse random graphs. Our main objective is to prove the existence of macroscopic loops, in the sense that a loop visits a positive proportion of the vertices. We develop a…

The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a key issue to compute it for massive graphs in the context of complex network analysis. However, known algorithms, including the ones…

Random graphs with a given degree sequence are often constructed using the configuration model, which yields a random multigraph. We may adjust this multigraph by a sequence of switchings, eventually yielding a simple graph. We show that,…

In a former paper we simplified the proof of a theorem on personalized random walk that is fundamental to graph nodes clustering and generalized it to bipartite graphs for a specific case where the proobability of random jump was…

The understanding of the immense and intricate topological structure of the World Wide Web (WWW) is a major scientific and technological challenge. This has been tackled recently by characterizing the properties of its representative graphs…

Patterns often appear in a variety of large, real-world networks, and interesting physical phenomena are often explained by network topology as in the case of the bow-tie structure of the World Wide Web, or the small world phenomenon in…

We explored the statistics of filtering of simple patterns on a number of deterministic and random graphs as a tractable simple example of information processing in complex systems. In this problem, multiple inputs map to the same output,…

We introduce a minimal extended evolving model for small-world networks which is controlled by a parameter. In this model the network growth is determined by the attachment of new nodes to already existing nodes that are geographically…

Inhomogeneous random graphs are fundamental models for real-world networks, where prescribed degrees are imposed as soft constraints. A common assumption in such models is that the degree distribution follows a power-law, capturing the…

In this work we introduce and study a nonlocal version of the PageRank. In our approach, the random walker explores the graph using longer excursions than just moving between neighboring nodes. As a result, the corresponding ranking of the…