Related papers: Rapid Bayesian Inference of Global Network Statist…
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…
This paper introduces a probabilistic approach for tracking the dynamics of unweighted and directed graphs using state-space models (SSMs). Unlike conventional topology inference methods that assume static graphs and generate point-wise…
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…
We propose an approximation for the first return time distribution of random walks on undirected networks. We combine a message-passing solution with a mean-field approximation, to account for the short- and long-term behaviours…
Estimating distributions of node characteristics (labels) such as number of connections or citizenship of users in a social network via edge and node sampling is a vital part of the study of complex networks. Due to its low cost, sampling…
We study several bayesian inference problems for irreversible stochastic epidemic models on networks from a statistical physics viewpoint. We derive equations which allow to accurately compute the posterior distribution of the time…
I start by reviewing some basic properties of random graphs. I then consider the role of random walks in complex networks and show how they may be used to explain why so many long tailed distributions are found in real data sets. The key…
We propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…
Random walks are the simplest way to explore or search a graph, and have revealed a very useful tool to investigate and characterize the structural properties of complex networks from the real world, e.g. they have been used to identify the…
Random walks constitute a fundamental mechanism for a large set of dynamics taking place on networks. In this article, we study random walks on weighted networks with an arbitrary degree distribution, where the weight of an edge between two…
In this paper, we present an overview of different types of random walk strategies with local and non-local transitions on undirected connected networks. We present a general approach to analyzing these strategies by defining the dynamics…
Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…
Efficient techniques to navigate networks with local information are fundamental to sample large-scale online social systems and to retrieve resources in peer-to-peer systems. Biased random walks, i.e. walks whose motion is biased on…
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…
We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width. Graph methods…
In this paper, we introduce a novel, general purpose, technique for faster sampling of nodes over an online social network. Specifically, unlike traditional random walk which wait for the convergence of sampling distribution to a…
Many network analysis and graph learning techniques are based on models of random walks which require to infer transition matrices that formalize the underlying stochastic process in an observed graph. For weighted graphs, it is common to…
We present a Bayesian formulation of weighted stochastic block models that can be used to infer the large-scale modular structure of weighted networks, including their hierarchical organization. Our method is nonparametric, and thus does…
The objective of this paper is to study the characteristics (geometric and otherwise) of very large attribute based undirected networks. Real-world networks are often very large and fast evolving. Their analysis and understanding present a…
Most empirical studies of complex networks do not return direct, error-free measurements of network structure. Instead, they typically rely on indirect measurements that are often error-prone and unreliable. A fundamental problem in…