Related papers: Estimating the Parameters of the Waxman Random Gra…
For stationary signals in time the weak law of large numbers (WLLN) states that ensemble and realization averages are within e of each other with a probability of order O(1/Ne^2) when considering N signal components. The graph WLLN…
We introduce a method for the theoretical analysis of exponential random graph models. The method is based on a large-deviations approximation to the normalizing constant shown to be consistent using theory developed by Chatterjee and…
Extreme value distributions are routinely employed to assess risks connected to extreme events in a large number of applications. They typically are two- or three- parameter distributions: the inference can be unstable, which is…
Using random walks for sampling has proven advantageous in assessing the characteristics of large and unknown social networks. Several algorithms based on random walks have been introduced in recent years. In the practical application of…
Graph embedding has recently gained momentum in the research community, in particular after the introduction of random walk and neural network based approaches. However, most of the embedding approaches focus on representing the local…
Consider the time T_oz when the random walk on a weighted graph started at the vertex o first hits the vertex set z. We present lower bounds for T_oz in terms of the volume of z and the graph distance between o and z. The bounds are for…
Graph randomization techniques play a crucial role in network analysis, allowing researchers to assess the statistical significance of observed network properties and distinguish meaningful patterns from random fluctuations. In this survey…
We introduce a natural generalization of the Erd\H{o}s-R\'enyi random graph model in which random instances of a fixed motif are added independently. The binomial random motif graph $G(H,n,p)$ is the random (multi)graph obtained by adding…
We propose a random walks based model to generate complex networks. Many authors studied and developed different methods and tools to analyze complex networks by random walk processes. Just to cite a few, random walks have been adopted to…
Graph Machine Learning (GML) has numerous applications, such as node/graph classification and link prediction, in real-world domains. Providing human-understandable explanations for GML models is a challenging yet fundamental task to foster…
We develop approximate estimation methods for exponential random graph models (ERGMs), whose likelihood is proportional to an intractable normalizing constant. The usual approach approximates this constant with Monte Carlo simulations,…
Motivated by low energy consumption in geographic routing in wireless networks, there has been recent interest in determining bounds on the length of edges in the Delaunay graph of randomly distributed points. Asymptotic results are known…
Graph Sampling provides an efficient yet inexpensive solution for analyzing large graphs. While extracting small representative subgraphs from large graphs, the challenge is to capture the properties of the original graph. Several sampling…
Binomial random intersection graphs can be used as parsimonious statistical models of large and sparse networks, with one parameter for the average degree and another for transitivity, the tendency of neighbours of a node to be connected.…
We propose a non-parametric link prediction algorithm for a sequence of graph snapshots over time. The model predicts links based on the features of its endpoints, as well as those of the local neighborhood around the endpoints. This allows…
This work will appear as a chapter in a forthcoming volume titled "Topics in Probabilistic Graph Theory". A theory of scaling limits for random graphs has been developed in recent years. This theory gives access to the large-scale geometric…
Structured output prediction is an important machine learning problem both in theory and practice, and the max-margin Markov network (\mcn) is an effective approach. All state-of-the-art algorithms for optimizing \mcn\ objectives take at…
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…
The paper demonstrates the use of LASSO-based estimation in network models. Taking the Exponential Random Graph Model (ERGM) as a flexible and widely used model for network data analysis, the paper focuses on the question of how to specify…
In this paper we introduce two Bayesian estimators for learning the parameters of the Gamma distribution. The first algorithm uses a well known unnormalized conjugate prior for the Gamma shape and the second one uses a non-linear…