Related papers: Structural Balance and Random Walks on Complex Net…
Random walks play an important role in probing the structure of complex networks. On traditional networks, they can be used to extract community structure, understand node centrality, perform link prediction, or capture the similarity…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…
Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical…
A continuous-time quantum walk is investigated on complex networks with the characteristic property of community structure, which is shared by most real-world networks. Motivated by the prospect of viable quantum networks, I focus on the…
Network models have been widely used to study diverse systems and analyze their dynamic behaviors. Given the structural variability of networks, an intriguing question arises: Can we infer the type of system represented by a network based…
The importance of structured, complex connectivity patterns found in several real-world systems is to a great extent related to their respective effects in constraining and even defining the respective dynamics. Yet, while complex networks…
We present measures, models and link prediction algorithms based on the structural balance in signed social networks. Certain social networks contain, in addition to the usual 'friend' links, 'enemy' links. These networks are called signed…
This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…
We review the main tools which allow for the statistical characterization of weighted networks. We then present two case studies, the airline connection network and the scientific collaboration network, which are representative of critical…
In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly…
We study the properties of discrete-time random walks on networks formed by randomly interconnected cliques, namely, random networks of cliques. Our purpose is to derive the parameters that define the network structure -- specifically, the…
In many studies, it is common to use binary (i.e., unweighted) edges to examine networks of entities that are either adjacent or not adjacent. Researchers have generalized such binary networks to incorporate edge weights, which allow one to…
Several interesting approaches have been reported in the literature on complex networks, random walks, and hierarchy of graphs. While many of these works perform random walks on stable, fixed networks, in the present work we address the…
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links.…
Most networks encountered in nature, society, and technology have weighted edges, representing the strength of the interaction/association between their vertices. Randomizing the structure of a network is a classic procedure used to…
Hypergraphs are used in machine learning to model higher-order relationships in data. While spectral methods for graphs are well-established, spectral theory for hypergraphs remains an active area of research. In this paper, we use random…
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…
The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of…
The segregated regions of the mammalian cerebral cortex and thalamus form an extensive and complex network, whose structure and function are still only incompletely understood. The present article describes an application of the concepts of…
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…