Related papers: On the Asymptotic Convergence of Subgraph Generate…
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…
We define a general class of network formation models, Statistical Exponential Random Graph Models (SERGMs), that nest standard exponential random graph models (ERGMs) as a special case. We provide the first general results on when these…
We introduce a new centrality measure that characterizes the participation of each node in all subgraphs in a network. Smaller subgraphs are given more weight than larger ones, which makes this measure appropriate for characterizing network…
Score-based graph generative models (SGGMs) have proven effective in critical applications such as drug discovery and protein synthesis. However, their theoretical behavior, particularly regarding convergence, remains underexplored. Unlike…
Random matrix theory has played an important role in recent work on statistical network analysis. In this paper, we review recent results on regimes of concentration of random graphs around their expectation, showing that dense graphs…
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…
We study the expected adjacency matrix of a uniformly random multigraph with fixed degree sequence $\mathbf{d} \in \mathbb{Z}_+^n$. This matrix arises in a variety of analyses of networked data sets, including modularity-maximization and…
A graph generative model defines a distribution over graphs. One type of generative model is constructed by autoregressive neural networks, which sequentially add nodes and edges to generate a graph. However, the likelihood of a graph under…
We consider the problem of graph generation guided by network statistics, i.e., the generation of graphs which have given values of various numerical measures that characterize networks, such as the clustering coefficient and the number of…
Hypergraphs that can depict interactions beyond pairwise edges have emerged as an appropriate representation for modeling polyadic relations in complex systems. With the recent surge of interest in researching hypergraphs, the centrality…
Detecting communities in high-dimensional graphs can be achieved by applying random matrix theory where the adjacency matrix of the graph is modeled by a Stochastic Block Model (SBM). However, the SBM makes an unrealistic assumption that…
Consider any random graph model where potential edges appear independently, with possibly different probabilities, and assume that the minimum expected degree is omega(ln n). We prove that the adjacency matrix and the Laplacian of that…
Unsupervised graph representation learning aims to learn low-dimensional node embeddings without supervision while preserving graph topological structures and node attributive features. Previous graph neural networks (GNN) require a large…
Link prediction is a key aspect of graph machine learning, with applications as diverse as disease prediction, social network recommendations, and drug discovery. It involves predicting new links that may form between network nodes. Despite…
Dynamic graphs are extensively employed for detecting anomalous behavior in nodes within the Internet of Things (IoT). Graph generative models are often used to address the issue of imbalanced node categories in dynamic graphs.…
Social studies researchers use graphs to model group activities in social networks. An important property in this context is the centrality of a vertex: the inverse of the average distance to each other vertex. We describe a randomized…
Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…
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.…
The exponential random graph model (ERGM) is a central object in the study of clustering properties in social networks as well as canonical ensembles in statistical physics. Despite some breakthrough works in the mathematical understanding…
We propose and investigate a unifying class of sparse random graph models, based on a hidden coloring of edge-vertex incidences, extending an existing approach, Random graphs with a given degree distribution, in a way that admits a…