Related papers: Weighted Exponential Random graph models: Scope an…

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 structure of large-scale social networks has predominantly been articulated using generative models, a form of average-case analysis. This chapter surveys recent proposals of more robust models of such networks. These models posit…

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…

A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…

The statistical mechanics of spin models, such as the Ising or Potts models, on generic random graphs can be formulated economically by considering the N --> 1 limit of Hermitian matrix models. In this paper we consider the N --> 1 limit in…

Mechanistic network models specify the mechanisms by which networks grow and change, allowing researchers to investigate complex systems using both simulation and analytical techniques. Unfortunately, it is difficult to write likelihoods…

An important problem in network analysis is predicting a node attribute using both network covariates, such as graph embedding coordinates or local subgraph counts, and conventional node covariates, such as demographic characteristics.…

Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…

Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There is, however, a subtle difference between networks where weights are continuos…

Exponential Random Graph Models (ERGM) behave peculiar in large networks with thousand(s) of actors (nodes). Standard models containing two-star or triangle counts as statistics are often unstable leading to completely full or empty…

This article investigates emergence and complexity in complex systems that can share information on a network. To this end, we use a theoretical approach from information theory, computability theory, and complex networks. One key studied…

A variety of statistical graphical models have been defined to represent the conditional independences underlying a random vector of interest. Similarly, many different graphs embedding various types of preferential independences, as for…

We obtain several sharp spectral bounds, approximations, and exact values for the isoperimetric number and related edge-expansion parameters of graphs. Our results focus on graph powers and on families of graphs with rich algebraic or…

The modeling and analysis of networks and network data has seen an explosion of interest in recent years and represents an exciting direction for potential growth in statistics. Despite the already substantial amount of work done in this…

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…

We develop a statistical theory to characterize correlations in weighted networks. We define the appropriate metrics quantifying correlations and show that strictly uncorrelated weighted networks do not exist due to the presence of…

Paper proposes a model of large networks based on a random preferential attachment graph with addition of complete subgraphs (cliques). The proposed model refers to models of random graphs following the nonlinear preferential attachment…

We investigate the behavior of vertex-weighted exponential random graphs. We show that vertex-weighted exponential random graphs with edge weights induced by products of independent vertex weights are approximate mixtures of graphs whose…

Modeling power transmission networks is an important area of research with applications such as vulnerability analysis, study of cascading failures, and location of measurement devices. Graph-theoretic approaches have been widely used to…