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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…
Recently, the authors have proposed a new approach to the theory of random metrics, making an explicit link between probability measures on the space of metrics on a Kahler manifold and random matrix models. We consider simple examples of…
In this thesis, which is supervised by Dr. David Penman, we examine random interval graphs. Recall that such a graph is defined by letting $X_{1},\ldots X_{n},Y_{1},\ldots Y_{n}$ be $2n$ independent random variables, with uniform…
Web crawlers are used by internet search engines to gather information about the web graph. In this paper we investigate a simple process which models such software by walking around the vertices of a graph. Once initial random vertex…
We characterize the existence of the maximum likelihood estimator for discrete exponential families. Our criterion is simple to apply as we show in various settings, most notably for exponential models of random graphs. As an application,…
Various recent proposals increase the distinguishing power of Graph Neural Networks GNNs by propagating features between $k$-tuples of vertices. The distinguishing power of these "higher-order'' GNNs is known to be bounded by the…
D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…
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 paper we consider a population process evolving on a dynamic random graph. The dynamic random graph is an Erd\H{o}s--R\'enyi graph that is resampled every time unit, independently of the previous ones, with `edge existence…
Distributions following a power-law are an ubiquitous phenomenon. Methods for determining the exponent of a power-law tail by graphical means are often used in practice but are intrinsically unreliable. Maximum likelihood estimators for the…
Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…
Graph-theoretic methods have seen wide use throughout the literature on multi-agent control and optimization. When communications are intermittent and unpredictable, such networks have been modeled using random communication graphs. When…
The maximum likelihood threshold of a graph is the smallest number of data points that guarantees that maximum likelihood estimates exist almost surely in the Gaussian graphical model associated to the graph. We show that this graph…
The famous Watts-Strogatz (WS) small-world network model does not approach the Erd\H{o}s-R\'enyi (ER) random graph model in the limit of total randomization which can lead to confusion and complicates certain analyses. In this paper we…
Random graph matching refers to recovering the underlying vertex correspondence between two random graphs with correlated edges; a prominent example is when the two random graphs are given by Erd\H{o}s-R\'{e}nyi graphs $G(n,\frac{d}{n})$.…
Increasing the connectivity of a graph is a pivotal challenge in robust network design. The weighted connectivity augmentation problem is a common version of the problem that takes link costs into consideration. The problem is then to find…
The girth of a graph, i.e. the length of its shortest cycle, is a fundamental graph parameter. Unfortunately all known algorithms for computing, even approximately, the girth and girth-related structures in directed weighted $m$-edge and…
I propose an estimation algorithm for Exponential Random Graph Models (ERGM), a popular statistical network model for estimating the structural parameters of strategic network formation in economics and finance. Existing methods often…
Associated to each graph G is a Gaussian graphical model. Such models are often used in high-dimensional settings, i.e. where there are relatively few data points compared to the number of variables. The maximum likelihood threshold of a…
Within network analysis, the analytical maximum entropy framework has been very successful for different tasks as network reconstruction and filtering. In a recent paper, the same framework was used for link-prediction for monopartite…