Related papers: Entropy of Spatial Network Ensembles
A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph into a large network. We propose two complementary MCMC algorithms for…
In this paper we propose a distributed algorithm for the estimation and control of the connectivity of ad-hoc networks in the presence of a random topology. First, given a generic random graph, we introduce a novel stochastic power…
In this paper, we reveal the relationship between entropy rate and the congestion in complex network and solve it analytically for special cases. Finding maximizing entropy rate will lead to an improvement of traffic efficiency, we propose…
Following [6,12], we study coupled map networks over arbitrary finite graphs. An estimate from below for a topological entropy of a perturbed coupled map network via a topological entropy of an unperturbed network by making use of the…
In this article we give an in depth overview of the recent advances in the field of equilibrium networks. After outlining this topic, we provide a novel way of defining equilibrium graph (network) ensembles. We illustrate this concept on…
We study the entanglement entropy of a random tensor network (RTN) using tools from free probability theory. Random tensor networks are simple toy models that help the understanding of the entanglement behavior of a boundary region in the…
A wide variety of complex networks (social, biological, information etc.) exhibit local clustering with substantial variation in the clustering coefficient (the probability of neighbors being connected). Existing models of large graphs…
Spatial networks, in which nodes and edges are embedded in space, play a vital role in the study of complex systems. For example, many social networks attach geo-location information to each user, allowing the study of not only topological…
We investigate the entanglement of the ground state in the quantum networks that their nodes are considered as quantum harmonic oscillators. To this aim, the Schmidt numbers and entanglement entropy between two arbitrary partitions of a…
When discussing urban life, pedestrian accessibility to all main services is crucial for fostering social interactions, promoting healthy lifestyles, and reducing pollution. This is especially relevant in coherent urban agglomerations like…
Potentially influential spaces in the spatial networks of cities can be detected by means of the entropy participation ratios. Local (connectivity) and global (centrality) entropies are considered. While the connectivity entropy has a…
For various purposes and, in particular, in the context of data compression, a graph can be examined at three levels. Its structure can be described as the unlabeled version of the graph; then the labeling of its structure can be added; and…
We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…
Random geometric graphs are random graph models defined on metric spaces. Such a model is defined by first sampling points from a metric space and then connecting each pair of sampled points with probability that depends on their distance,…
We review mathematically tractable models for connected networks on random points in the plane, emphasizing the class of proximity graphs which deserves to be better known to applied probabilists and statisticians. We introduce and motivate…
We study models of weighted exponential random graphs in the large network limit. These models have recently been proposed to model weighted network data arising from a host of applications including socio-econometric data such as migration…
Geometry can be used to explain many properties commonly observed in real networks. It is therefore often assumed that real networks, especially those with high average local clustering, live in an underlying hidden geometric space.…
We investigate the increasingly prominent task of jointly inferring multiple networks from nodal observations. While most joint inference methods assume that observations are available at all nodes, we consider the realistic and more…
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…
A very popular class of models for networks posits that each node is represented by a point in a continuous latent space, and that the probability of an edge between nodes is a decreasing function of the distance between them in this latent…