Related papers: Metric structure of random networks
Mapping the Internet generally consists in sampling the network from a limited set of sources by using traceroute-like probes. This methodology, akin to the merging of different spanning trees to a set of destination, has been argued to…
The objective of this paper is to study the characteristics (geometric and otherwise) of very large attribute based undirected networks. Real-world networks are often very large and fast evolving. Their analysis and understanding present a…
In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the…
The global structure of the minimal spanning tree (MST) is expected to be universal for a large class of underlying random discrete structures. However, very little is known about the intrinsic geometry of MSTs of most standard models, and…
Redundancy needs more precise characterization as it is a major factor in the evolution and robustness of networks of multivariate interactions. We investigate the complexity of such interactions by inferring a connection transitivity that…
We consider the problem of adding a fixed number of new edges to an undirected graph in order to minimize the diameter of the augmented graph, and under the constraint that the number of edges added for each vertex is bounded by an integer.…
Correlations may affect propagation processes on complex networks. To analyze their effect, it is useful to build ensembles of networks constrained to have a given value of a structural measure, such as the degree-degree correlation $r$,…
Recall that Janson showed that if the edges of the complete graph $K_n$ are assigned exponentially distributed independent random weights, then the expected length of a shortest path between a fixed pair of vertices is asymptotically equal…
The metric dimension of a graph $G$ is the minimum number of vertices in a subset $S$ of the vertex set of $G$ such that all other vertices are uniquely determined by their distances to the vertices in $S$. In this paper we investigate the…
We propose a novel Bayesian methodology which uses random walks for rapid inference of statistical properties of undirected networks with weighted or unweighted edges. Our formalism yields high-accuracy estimates of the probability…
The Thorup-Zwick (TZ) routing scheme is the first generic stretch-3 routing scheme delivering a nearly optimal local memory upper bound. Using both direct analysis and simulation, we calculate the stretch distribution of this routing scheme…
Random walks constitute a fundamental mechanism for a large set of dynamics taking place on networks. In this article, we study random walks on weighted networks with an arbitrary degree distribution, where the weight of an edge between two…
We investigate certain structural properties of random interdependent networks. We start by studying a property known as $r$-robustness, which is a strong indicator of the ability of a network to tolerate structural perturbations and…
We have studied transportation network, namely a road network of the Moscow region and airline network of the Russian Federation. We have constructed corresponding networks and studied degree distribution and length distribution for these…
We examine the global organization of heterogeneous equilibrium networks consisting of a number of well distinguished interconnected parts--``communities'' or modules. We develop an analytical approach allowing us to obtain the statistics…
A random intersection graph is constructed by independently assigning a subset of a given set of objects $W,$ to each vertex of the vertex set $V$ of a simple graph $G.$ There is an edge between two vertices of $V,$ iff their respective…
Small world models are networks consisting of many local links and fewer long range `shortcuts'. In this paper, we consider some particular instances, and rigorously investigate the distribution of their inter--point network distances. Our…
In a model of a connected network on random points in the plane, one expects that the mean length of the shortest route between vertices at distance $r$ apart should grow only as $O(r)$ as $r \to \infty$, but this is not always easy to…
We show how scale-free degree distributions can emerge naturally from growing networks by using random walks for selecting vertices for attachment. This result holds for several variants of the walk algorithm and for a wide range of…
Metric graph properties lie in the heart of the analysis of complex networks, while in this paper we study their convexity through mathematical definition of a convex subgraph. A subgraph is convex if every geodesic path between the nodes…