Related papers: Connectivity and Structure in Large Networks

We derive the sampling properties of random networks based on weights whose pairwise products parameterize independent Bernoulli trials. This enables an understanding of many degree-based network models, in which the structure of realized…

Random K-out graphs are used in several applications including modeling by sensor networks secured by the random pairwise key predistribution scheme, and payment channel networks. The random K-out graph with $n$ nodes is constructed as…

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…

Random graph models have played a dominant role in the theoretical study of networked systems. The Poisson random graph of Erdos and Renyi, in particular, as well as the so-called configuration model, have served as the starting point for…

Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…

We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…

Connectivity of wireless sensor networks (WSNs) is a fundamental global property expected to be maintained even though some sensor nodes are at fault. In this paper, we investigate the connectivity of random geometric graphs (RGGs) in the…

Small-world networks are the focus of recent interest because they appear to circumvent many of the limitations of either random networks or regular lattices as frameworks for the study of interaction networks of complex systems. Here, we…

In this work we introduce Dynamic Random Geometric Graphs as a basic rough model for mobile wireless sensor networks, where communication distances are set to the known threshold for connectivity of static random geometric graphs. We…

This research establishes that many real-world networks exhibit bounded expansion, a strong notion of structural sparsity, and demonstrates that it can be leveraged to design efficient algorithms for network analysis. We analyze several…

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…

We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the…

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…

We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time…

We introduce a class of random graphs that we argue meets many of the desiderata one would demand of a model to serve as the foundation for a statistical analysis of real-world networks. The class of random graphs is defined by a…

Triangles are an important building block and distinguishing feature of real-world networks, but their structure is still poorly understood. Despite numerous reports on the abundance of triangles, there is very little information on what…

We consider the size and structure of the automorphism groups of a variety of empirical `real-world' networks and find that, in contrast to classical random graph models, many real-world networks are richly symmetric. We relate automorphism…

We analyse graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size…

The degrees are a classical and relevant way to study the topology of a network. They can be used to assess the goodness-of-fit for a given random graph model. In this paper we introduce goodness-of-fit tests for two classes of models.…

A wide array of random graph models have been postulated to understand properties of observed networks. Typically these models have a parameter $t$ and a critical time $t_c$ when a giant component emerges. It is conjectured that for a large…