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We investigate the computational complexity of the exponential random graph model (ERGM) commonly used in social network analysis. This model represents a probability distribution on graphs by setting the log-likelihood of generating a…
A new modelling approach for the analysis of weighted networks with ordinal/polytomous dyadic values is introduced. Specifically, it is proposed to model the weighted network connectivity structure using a hierarchical multilayer…
Recent advances in computational methods for intractable models have made network data increasingly amenable to statistical analysis. Exponential random graph models (ERGMs) emerged as one of the main families of models capable of capturing…
In this work, a novel model of the random geometric graph (RGG), namely the isotropic random geometric graph (IRGG) has been developed and its topological properties in two dimensions have been studied in details. The defining…
The stochastic block model is a natural model for studying community detection in random networks. Its clustering properties have been extensively studied in the statistics, physics and computer science literature. Recently this area has…
Graph-theoretic tools and techniques have seen wide use in the multi-agent systems literature, and the unpredictable nature of some multi-agent communications has been successfully modeled using random communication graphs. Across both…
The hyperbolic random graph model (HRG) has proven useful in the analysis of scale-free networks, which are ubiquitous in many fields, from social network analysis to biology. However, working with this model is algorithmically and…
We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…
In this article, we analyze the limiting eigenvalue distribution (LED) of random geometric graphs (RGGs). The RGG is constructed by uniformly distributing $n$ nodes on the $d$-dimensional torus $\mathbb{T}^d \equiv [0, 1]^d$ and connecting…
Modeling dynamic graphs, such as those found in social networks, recommendation systems, and e-commerce platforms, is crucial for capturing evolving relationships and delivering relevant insights over time. Traditional approaches primarily…
The geometric block model is a recently proposed generative model for random graphs that is able to capture the inherent geometric properties of many community detection problems, providing more accurate characterizations of practical…
Learning community structures in graphs has broad applications across scientific domains. While graph neural networks (GNNs) have been successful in encoding graph structures, existing GNN-based methods for community detection are limited…
Soft Random Geometric Graphs (SRGGs) have been widely applied to various models including those of wireless sensor, communication, social and neural networks. SRGGs are constructed by randomly placing nodes in some space and making pairwise…
We introduce two models of inclusion hierarchies: Random Graph Hierarchy (RGH) and Limited Random Graph Hierarchy (LRGH). In both models a set of nodes at a given hierarchy level is connected randomly, as in the Erd\H{o}s-R\'{e}nyi random…
We develop a new class of random graph models for the statistical estimation of network formation -- subgraph generated models (SUGMs). Various subgraphs -- e.g., links, triangles, cliques, stars -- are generated and their union results in…
Socially-intelligent agents are of growing interest in artificial intelligence. To this end, we need systems that can understand social relationships in diverse social contexts. Inferring the social context in a given visual scene not only…
Similarity search is a fundamental building block for information retrieval on a variety of datasets. The notion of a neighbor is often based on binary considerations, such as the k nearest neighbors. However, considering that data is often…
We propose an interdependent random geometric graph (RGG) model for interdependent networks. Based on this model, we study the robustness of two interdependent spatially embedded networks where interdependence exists between geographically…
Understanding overlapping community structures is crucial for network analysis and prediction. AGM (Affiliation Graph Model) is one of the favorite models for explaining the densely overlapped community structures. In this paper, we…
Many popular models from the networks literature can be viewed through a common lens of contingency tables on network dyads, resulting in \emph{log-linear ERGMs}: exponential family models for random graphs whose sufficient statistics are…