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We consider the problem of dominating set-based virtual backbone used for routing in asymmetric wireless ad-hoc networks. These networks have non-uniform transmission ranges and are modeled using the well-established disk graphs. The…
In this work, we study the correlation between attribute sets and the occurrence of dense subgraphs in large attributed graphs, a task we call structural correlation pattern mining. A structural correlation pattern is a dense subgraph…
We couple projective limits of probability measures to direct limits of their symmetry groups. We show that the direct limit group is the group of symmetries of the projective limit probability measure. If projective systems of probability…
In our recent works, we developed a probabilistic framework for structural analysis in undirected networks. The key idea of that framework is to sample a network by a symmetric bivariate distribution and then use that bivariate distribution…
In the computational study of political redistricting, feasibility necessitates the use of a discretization of regions such as states, counties, and towns. In nearly all cases, researchers use a dual graph, whose vertices represent small…
A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square [0,1]^2. The topological properties of the…
The random graph model has recently been extended to a random preferential attachment graph model, in order to enable the study of general asymptotic properties in network types that are better represented by the preferential attachment…
Decentralized learning strategies allow a collection of agents to learn efficiently from local data sets without the need for central aggregation or orchestration. Current decentralized learning paradigms typically rely on an averaging…
Low density graphs are considered to be a realistic graph class for modelling road networks. It has advantages over other popular graph classes for road networks, such as planar graphs, bounded highway dimension graphs, and spanners. We…
We study the typical behavior of a generalized version of Google's PageRank algorithm on a large family of inhomogeneous random digraphs. This family includes as special cases directed versions of classical models such as the…
Proximity graph-based methods have emerged as a leading paradigm for approximate nearest neighbor (ANN) search in the system community. This paper presents fresh insights into the theoretical foundation of these methods. We describe an…
A class of random graph models is considered, combining features of exponential-family models and latent structure models, with the goal of retaining the strengths of both of them while reducing the weaknesses of each of them. An open…
Distances in a network capture relations between nodes and are the basis of centrality, similarity, and influence measures. Often, however, the relevance of a node $u$ to a node $v$ is more precisely measured not by the magnitude of the…
We study fundamental graph parameters such as the Diameter and Radius in directed graphs, when distances are measured using a somewhat unorthodox but natural measure: the distance between $u$ and $v$ is the minimum of the shortest path…
Statistical field theory methods have been very successful with a number of random graph and random matrix problems, but it is challenging to apply these methods to graphs with prescribed degree sequences due to the extensive number of…
In this article, we extend a statistical test of graph clusterability, the $\delta$ test, to directed graphs with no self loops. The $\delta$ test, originally designed for undirected graphs, is based on the premise that graphs with a…
Randomness or mutual independence is an important underlying assumption for most widely used statistical methods for circular data. Verifying this assumption is essential to ensure the validity and reliability of the resulting inferences.…
This contribution proposes a new approach towards developing a class of probabilistic methods for classifying attributed graphs. The key concept is random attributed graph, which is defined as an attributed graph whose nodes and edges are…
Graph sampling via crawling has become increasingly popular and important in the study of measuring various characteristics of large scale complex networks. While powerful, it is known to be challenging when the graph is loosely connected…
Density-based directed distances -- particularly known as divergences -- between probability distributions are widely used in statistics as well as in the adjacent research fields of information theory, artificial intelligence and machine…