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Learning properties of large graphs from samples has been an important problem in statistical network analysis since the early work of Goodman \cite{Goodman1949} and Frank \cite{Frank1978}. We revisit a problem formulated by Frank…
The study of the topological structure of complex networks has fascinated researchers for several decades, and today we have a fairly good understanding of the types and reoccurring characteristics of many different complex networks.…
We study a class of growth algorithms for directed graphs that are candidate models for the evolution of genetic regulatory networks. The algorithms involve partial duplication of nodes and their links, together with innovation of new…
A probabilistic generative network model with $n$ nodes and $m$ overlapping layers is obtained as a superposition of $m$ mutually independent Bernoulli random graphs of varying size and strength. When $n$ and $m$ are large and of the same…
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…
Motivated in part by understanding average case analysis of fundamental algorithms in computer science, and in part by the wide array of network data available over the last decade, a variety of random graph models, with corresponding…
Complex networks, modeled as large graphs, received much attention during these last years. However, data on such networks is only available through intricate measurement procedures. Until recently, most studies assumed that these…
In this paper, we study a bipartite analogue of the `random graphs evolving by degrees' process. We are given a bipartitioned set of vertices $V$ into two disjoint parts ${L}$ and ${R}$ and possibly unequal positive constants $\alpha$ and…
We study the size of the largest biconnected components in sparse Erd\H{o}s-R\'enyi graphs with finite connectivity and Barab\'asi-Albert graphs with non-integer mean degree. Using a statistical-mechanics inspired Monte Carlo approach we…
Random graph models are used to describe the complex structure of real-world networks in diverse fields of knowledge. Studying their behavior and fitting properties are still critical challenges, that in general, require model specific…
The vertex-random graphs called proximity catch digraphs (PCDs) have been introduced recently and have applications in pattern recognition and spatial pattern analysis. A PCD is a random directed graph (i.e., digraph) which is constructed…
Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical…
Unsupervised anomaly detection aims to identify anomalous samples from highly complex and unstructured data, which is pervasive in both fundamental research and industrial applications. However, most existing methods neglect the complex…
The degree distributions of complex networks are usually considered to be power law. However, it is not the case for a large number of them. We thus propose a new model able to build random growing networks with (almost) any wanted degree…
The goal of is to study how increased variability in the degree distribution impacts the global connectivity properties of a large network. We approach this question by modeling the network as a uniform random graph with a given degree…
This study introduces a novel model that effectively captures asymmetric structures in multivariate contingency tables with ordinal categories. Leveraging the principle of maximum entropy, our approach employs f-divergence to provide a…
In this paper we study the synchronization properties of random geometric graphs. We show that the onset of synchronization takes place roughly at the same value of the order parameter that a random graph with the same size and average…
We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement…
Random graph models are a recurring tool-of-the-trade for studying network structural properties and benchmarking community detection and other network algorithms. Moreover, they serve as test-bed generators for studying diffusion and…
We consider a random geometric hypergraph model based on an underlying bipartite graph. Nodes and hyperedges are sampled uniformly in a domain, and a node is assigned to those hyperedges that lie with a certain radius. From a modelling…