Related papers: It's a Small World for Random Surfers
We give exact relations which are valid for small-world networks (SWN's) with a general `degree distribution', i.e the distribution of nearest-neighbor connections. For the original SWN model, we illustrate how these exact relations can be…
Robertson and Seymour's celebrated Graph Minor Theorem states that graphs are well-quasi-ordered by the minor relation. Unlike the minor relation, the topological minor relation does not well-quasi-order graphs in general. Among all known…
We consider the problem of estimating the graph size, where one is given only local access to the graph. We formally define a query model in which one starts with a \emph{seed} node and is allowed to make queries about neighbours of nodes…
Navigation process is studied on a variant of the Watts-Strogatz small world network model embedded on a square lattice. With probability $p$, each vertex sends out a long range link, and the probability of the other end of this link…
In this paper we prove that if a pair of graphs G,H have senders, then they necessarily have connected minimal senders; we also prove that given two fixed graphs that are either 3-connected or triangles there are minimal (G,H)-senders with…
We present a new notion of limits of weighted directed graphs of growing size based on convergence of their random quotients. These limits are specified in terms of random exchangeable measures on the unit square. We call our limits…
Specify a randomized algorithm that, given a very large graph or network, extracts a random subgraph. What can we learn about the input graph from a single subsample? We derive laws of large numbers for the sampler output, by relating…
Recently, Watts and Strogatz introduced the so-called small-world networks in order to describe systems which combine simultaneously properties of regular and of random lattices. In this work we study diffusion processes defined on such…
We compare two link analysis ranking methods of web pages in a site. The first, called Site Rank, is an adaptation of PageRank to the granularity of a web site and the second, called Popularity Rank, is based on the frequencies of user…
Two new classes of networks are introduced that resemble small-world properties. These networks are recursively constructed but retain a fixed, regular degree. They consist of a one-dimensional lattice backbone overlayed by a hierarchical…
We consider a class of growing random graphs obtained by creating vertices sequentially one by one: at each step, we choose uniformly the neighbours of the newly created vertex; its degree is a random variable with a fixed but arbitrary…
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 expansion property. The Chung-Lu random graph…
The Small World phenomenon has inspired researchers across a number of fields. A breakthrough in its understanding was made by Kleinberg who introduced Rank Based Augmentation (RBA): add to each vertex independently an arc to a random…
The cover time of random walks on a graph has found wide practical applications in different fields of computer science, such as crawling and searching on the World Wide Web and query processing in sensor networks, with the application…
We find that the simple coupling of network growth to the position of a random walker on the network generates a traveling wave in the probability distribution of nodes visited by the walker. We argue that the entropy of this probability…
We study the dynamics of an epidemic-like model for the spread of a rumor on a small-world network. It has been shown that this model exhibits a transition between regimes of localization and propagation at a finite value of the network…
Theoretical analyses for graph learning methods often assume a complete observation of the input graph. Such an assumption might not be useful for handling any-size graphs due to the scalability issues in practice. In this work, we develop…
We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time…
We study separating systems of the edges of a graph where each member of the separating system is a path. We conjecture that every $n$-vertex graph admits a separating path system of size $O(n)$ and prove this in certain interesting special…
The topology of the Internet has typically been measured by sampling traceroutes, which are roughly shortest paths from sources to destinations. The resulting measurements have been used to infer that the Internet's degree distribution is…