Related papers: A Bayesian model for sparse graphs with flexible d…
In this paper, we present a simple model of scale-free networks that incorporates both preferential & random attachment and anti-preferential & random deletion at each time step. We derive the degree distribution analytically and show that…
Empirical evidence suggests that heavy-tailed degree distributions occurring in many real networks are well-approximated by power laws with exponents $\eta$ that may take values either less than and greater than two. Models based on various…
We find that scale-free random networks are excellently modeled by a deterministic graph. This graph has a discrete degree distribution (degree is the number of connections of a vertex) which is characterized by a power-law with exponent…
We study a recent model for edge exchangeable random graphs introduced by Crane and Dempsey; in particular we study asymptotic properties of the random simple graph obtained by merging multiple edges. We study a number of examples, and show…
Scale-free networks play a fundamental role in the study of complex networks and various applied fields due to their ability to model a wide range of real-world systems. A key characteristic of these networks is their degree distribution,…
Exponential random graphs are important to model the structure of real-world complex networks. Here we solve the two-star model with degree-degree correlations in the sparse regime. The model constraints the average correlation between the…
We introduce a random intersection graph process aimed at modeling sparse evolving affiliation networks that admit tunable (power law) degree distribution and assortativity and clustering coefficients. We show the asymptotic degree…
We introduce and study a class of exchangeable random graph ensembles. They can be used as statistical null models for empirical networks, and as a tool for theoretical investigations. We provide general theorems that carachterize the…
As the availability and importance of temporal interaction data--such as email communication--increases, it becomes increasingly important to understand the underlying structure that underpins these interactions. Often these interactions…
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…
Unreliable network data can cause community-detection methods to overfit and highlight spurious structures with misleading information about the organization and function of complex systems. Here we show how to detect significant flow-based…
In this paper we describe the emergence of scale-free degree distributions from statistical mechanics principles. We define an energy associated to a degree sequence as the logarithm of the number of indistinguishable simple networks it is…
We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be…
Empirical networks are often globally sparse, with a small average number of connections per node, when compared to the total size of the network. However, this sparsity tends not to be homogeneous, and networks can also be locally dense,…
Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast,…
We introduce a growing network model---the copying model---in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability $p$. When…
We study the node classification problem on feature-decorated graphs in the sparse setting, i.e., when the expected degree of a node is $O(1)$ in the number of nodes, in the fixed-dimensional asymptotic regime, i.e., the dimension of the…
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…
Many social and biological networks consist of communities - groups of nodes within which connections are dense, but between which connections are sparser. Recently, there has been considerable interest in designing algorithms for detecting…
We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…