Random walks are ubiquitous in the sciences, and they are interesting from both theoretical
and practical perspectives. They are one of the most fundamental types of stochastic …

We present a general theory which allows one to accurately evaluate the mean first-passage
time (FPT) for regular random walks in bounded domains, and its extensions to related first …

The availability of large data sets has allowed researchers to uncover complex properties
such as large-scale fluctuations and heterogeneities in many networks, leading to the …

This book discusses the study and analysis of the physical aspects of social systems and
models, inspired by the analogy with familiar models of physical systems and possible …

How long does it take a random walker to reach a given target point? This quantity, known
as a first-passage time (FPT), has led to a growing number of theoretical investigations over …

We explore the concepts of self-similarity, dimensionality, and (multi) scaling in a new family
of recursive scale-free nets that yield themselves to exact analysis through renormalization …

We present a general framework, applicable to a broad class of random walks on complex
networks, which provides a rigorous lower bound for the mean first-passage time of a …

We study numerically the ordering process of two very simple dynamical models for a two-
state variable on several topologies with increasing levels of heterogeneity in the degree …

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 …

We report on some recent developments in the search for optimal network topologies. First
we review some basic concepts on spectral graph theory, including adjacency and …