Related papers: Random graphs as models of networks

Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a…

Infectious disease remains, despite centuries of work to control and mitigate its effects, a major problem facing humanity. This paper reviews the mathematical modelling of infectious disease epidemics on networks, starting from the…

The theory of random graphs goes back to the late 1950s when Paul Erd\H{o}s and Alfr\'ed R\'enyi introduced the Erd\H{o}s-R\'enyi random graph. Since then many models have been developed, and the study of random graph models has become…

Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical…

One of the main characteristics of real-world networks is their large clustering. Clustering is one aspect of a more general but much less studied structural organization of networks, i.e. edge multiplicity, defined as the number of…

Nowadays, exponential random graphs (ERGs) are among the most widely-studied network models. Different analytical and numerical techniques for ERG have been developed that resulted in the well-established theory with true predictive power.…

In this paper we will provide an introductory understanding of random graph models, and matchings in the case of Erdos-Renyi random graphs. We will provide a synthesis of background theory to this end. We will further examine pertinent…

Traditional random graph models of networks generate networks that are locally tree-like, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly…

Real social networks are often compared to random graphs in order to assess whether their typological structure could be the result of random processes. However, an Erd\H{o}s-R\'enyi random graph in large scale is often lack of local…

Generalised degrees provide a natural bridge between local and global topological properties of networks. We define the generalised degree to be the number of neighbours of a node within one and two steps respectively. Tailored random graph…

Network analysis has become an increasingly prevalent research tool across a vast range of scientific fields. Here, we focus on the particular issue of comparing network statistics, i.e. graph-level measures of network structural features,…

Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. These include scale-free degree distributions, small-world structure and assortative mixing by…

Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…

Various approaches and measures from network analysis have been applied to granular and particulate networks to gain insights into their structural, transport, failure-propagation and other systems-level properties. In this article, we…

We discuss two sampling schemes for selecting random subnets from a network: Random sampling and connectivity dependent sampling, and investigate how the degree distribution of a node in the network is affected by the two types of sampling.…

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…

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…

In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…

A random network model which allows for tunable, quite general forms of clustering, degree correlation and degree distribution is defined. The model is an extension of the configuration model, in which stubs (half-edges) are paired to form…

We consider the problem of determining the proportion of edges that are discovered in an Erdos-Renyi graph when one constructs all shortest paths from a given source node to all other nodes. This problem is equivalent to the one of…