Related papers: Generalized entropies and open random and scale-fr…
A network is formed using the $N$ sites of an one-dimensional lattice in the shape of a ring as nodes and each node with the initial degree $k_{in}=2$. $N$ links are then introduced to this network, each link starts from a distinct node,…
We study Erd\"{o}s-R\'enyi random graphs with random weights associated with each link. We generate a new ``Supernode network'' by merging all nodes connected by links having weights below the percolation threshold (percolation clusters)…
We define the concept of dependence among multiple variables using maximum entropy techniques and introduce a graphical notation to denote the dependencies. Direct inference of information theoretic quantities from data uncovers…
We present a general holistic theory for the organization of complex networks, both human-engineered and naturally-evolved. Introducing concepts of value of interactions and satisfaction as generic network performance measures, we show that…
We consider random walks that start and are absorbed on the leaves of random networks and study the length of such walks. For the networks we investigate, Erdos-Renyi random graphs and Barabasi-Albert scale free networks, these walks are…
We propose a method of generating different scale-free networks, which has several input parameters in order to adjust the structure, so that they can serve as a basis for computer simulation of real-world phenomena. The topological…
Relations between Shannon entropy and Renyi entropies of integer order are discussed. For any N-point discrete probability distribution for which the Renyi entropies of order two and three are known, we provide an lower and an upper bound…
Reconstructing the structural connectivity between interacting units from observed activity is a challenge across many different disciplines. The fundamental first step is to establish whether or to what extent the interactions between the…
We analyze a distributed information network in which each node has access to the information contained in a limited set of nodes (its neighborhood) at a given time. A collective computation is carried out in which each node calculates a…
We propose a simple algorithm which produces a new category of networks, high dimensional random Apollonian networks, with small-world and scale-free characteristics. We derive analytical expressions for their degree distributions and…
Many real networks exhibit a layered structure in which links in each layer reflect the function of nodes on different environments. These multiple types of links are usually represented by a multiplex network in which each layer has a…
In this paper, we consider the problem of exploring structural regularities of networks by dividing the nodes of a network into groups such that the members of each group have similar patterns of connections to other groups. Specifically,…
We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly…
Random graph (RG) models play a central role in the complex networks analysis. They help to understand, control, and predict phenomena occurring, for instance, in social networks, biological networks, the Internet, etc. Despite a large…
What is the underlying mechanism leading to power-law degree distributions of many natural and artificial networks is still at issue. We consider that scale-free networks emerges from self-organizing process, and such a evolving model is…
The problem of defining a statistical ensemble of random graphs with an arbitrary connectivity distribution is discussed. Introducing such an ensemble is a step towards uderstanding the geometry of wide classes of graphs independently of…
How to evaluate the importance of nodes is essential in research of complex network. There are many methods proposed for solving this problem, but they still have room to be improved. In this paper, a new approach called local volume…
We present a method to construct a network null-model based on the maximum entropy principle and where the restrictions that the rich-club and the degree sequence impose are conserved. We show that the probability that two nodes share a…
This paper provides a necessary and sufficient condition for a random network with nodes Poissonly distributed on a unit square and a pair of nodes directly connected following a generic random connection model to be asymptotically almost…
We provide a framework for determining the centralities of agents in a broad family of random networks. Current understanding of network centrality is largely restricted to deterministic settings, but practitioners frequently use random…