Related papers: Degree distribution of shortest path trees and bia…
We consider distributed networks, such as peer-to-peer networks, whose structure can be manipulated by adjusting the rules by which vertices enter and leave the network. We focus in particular on degree distributions and show that, with…
We consider single-source shortest path algorithms that perform a sequence of relaxation steps whose ordering depends only on the input graph structure and not on its weights or the results of prior steps. Each step examines one edge of the…
We present analytical results for the distribution of shortest cycle lengths (DSCL) in random networks. The approach is based on the relation between the DSCL and the distribution of shortest path lengths (DSPL). We apply this approach to…
Consensus about the universality of the power law feature in complex networks is experiencing profound challenges. To shine fresh light on this controversy, we propose a generic theoretical framework in order to examine the power law…
We investigate the joint distribution of the vertex degrees in three models of random bipartite graphs. Namely, we can choose each edge with a specified probability, choose a specified number of edges, or specify the vertex degrees in one…
We consider an edge-weighted uniform random graph with a given degree sequence (Repeated Configuration Model) which is a useful approximation for many real-world networks. It has been observed that the vertices which are separated from the…
A well-known open problem on the behavior of optimal paths in random graphs in the strong disorder regime, formulated by statistical physicists, and supported by a large amount of numerical evidence over the last decade [31,32,38,70] is as…
In this paper we consider the optimization problem of generating graphs with a prescribed degree distribution, such that the correlation between the degrees of connected nodes, as measured by Spearman's rho, is minimal. We provide an…
We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the…
For a simple (unbiased) random walk on a connected graph with $n$ vertices, the cover time (the expected number of steps it takes to visit all vertices) is at most $O(n^3)$. We consider locally biased random walks, in which the probability…
The weight of the minimum spanning tree in a complete weighted graph with random edge weights is a well-known problem. For various classes of distributions, it is proved that the weight of the minimum spanning tree tends to a constant,…
We investigate a network model based on an infinite regular square lattice embedded in the Euclidean plane where the node connection probability is given by the geometrical distance of nodes. We show that the degree distribution in the…
We consider the infinite directed graph with vertices the set of integers ...,-2,-1,0,1,2,... . Let v be a random variable taking either finite values or value "minus infinity". Consider random weights v(j,k), indexed by pairs (j,k) of…
In this paper we study the degree sequence of the permutation graph $G_{\pi_n}$ associated with a sequence $\pi_n\in S_n$ of random permutations. Joint limiting distributions of the degrees are established using results from graph and…
In this paper, we revisit the problem of sampling edges in an unknown graph $G = (V, E)$ from a distribution that is (pointwise) almost uniform over $E$. We consider the case where there is some a priori upper bound on the arboriciy of $G$.…
A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…
Finding graph indices which are unbiased to network size and density is of high importance both within a given field and across fields for enhancing comparability of modern network science studies. The degree variance is an important metric…
We present a model for random simple graphs with a degree distribution that obeys a power law (i.e., is heavy-tailed). To attain this behavior, the edge probabilities in the graph are constructed from Bertoin-Fujita-Roynette-Yor (BFRY)…
Random spanning trees of a graph $G$ are governed by a corresponding probability mass distribution (or "law"), $\mu$, defined on the set of all spanning trees of $G$. This paper addresses the problem of choosing $\mu$ in order to utilize…
Empirical studies on the spatial structures in several real transport networks reveal that the distance distribution in these networks obeys power law. To discuss the influence of the power-law exponent on the network's structure and…