Related papers: Quantifying randomness in real networks
We study the statistical properties of large random networks with specified degree distributions. New techniques are presented for analyzing the structure of social networks. Specifically, we address the question of how many nodes exist at…
Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely…
The random graph of Erdos and Renyi is one of the oldest and best studied models of a network, and possesses the considerable advantage of being exactly solvable for many of its average properties. However, as a model of real-world networks…
Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…
Complex networks has been a hot topic of research over the past several years over crossing many disciplines, starting from mathematics and computer science and ending by the social and biological sciences. Random graphs were studied to…
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,…
Random networks are a powerful tool in the analytical modeling of complex networks as they allow us to write approximate mathematical models for diverse properties and behaviors of networks. One notable shortcoming of these models is that…
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical…
We study random graph models for directed acyclic graphs, an important class of networks that includes citation networks, food webs, and feed-forward neural networks among others. We propose two specific models, roughly analogous to the…
k-connectivity of random graphs is a fundamental property indicating reliability of multi-hop wireless sensor networks (WSN). WSNs comprising of sensor nodes with limited power resources are modeled by random graphs with unreliable nodes,…
We present a new, systematic approach for analyzing network topologies. We first introduce the dK-series of probability distributions specifying all degree correlations within d-sized subgraphs of a given graph G. Increasing values of d…
I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key…
Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet, and the network of followers on Twitter among many others. The challenge, however, is to create a network model that…
Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior…
One property of networks that has received comparatively little attention is hierarchy, i.e., the property of having vertices that cluster together in groups, which then join to form groups of groups, and so forth, up through all levels of…
k-connectivity is an important measure of network robustness and resilience to random faults and disruptions. We undertake both local and global approaches to k-connectivity and calculate closed form analytic formulas for the probability…
Randomized network ensembles are the null models of real networks and are extensivelly used to compare a real system to a null hypothesis. In this paper we study network ensembles with the same degree distribution, the same…
We propose a general approach to the description of spectra of complex networks. For the spectra of networks with uncorrelated vertices (and a local tree-like structure), exact equations are derived. These equations are generalized to the…
Based on a large dataset containing thousands of real-world networks ranging from genetic, protein interaction, and metabolic networks to brain, language, ecology, and social networks we search for defining structural measures of the…