The availability of large data sets have allowed researchers to uncover complex properties such as large scale fluctuations and heterogeneities in many networks which have lead to the breakdown of standard theoretical frameworks and models. Until recently these systems were considered as haphazard sets of points and connections. Recent advances have generated a vigorous research effort in understanding the effect of complex connectivity patterns on dynamical phenomena. For example, a vast number of everyday systems, from the brain to ecosystems, power grids and the Internet, can be represented as large complex networks. This new and recent account presents a comprehensive explanation of these effects.
This text is about spreading of information and influence in complex networks. Although previously considered similar and modeled in parallel approaches, there is now experimental evidence that epidemic and social spreading work in subtly different ways. While previously explored through modeling, there is currently an explosion of work on revealing the mechanisms underlying complex contagion based on big data and data-driven approaches. This volume consists of four parts. Part 1 is an Introduction, providing an accessible summary of the state of the art. Part 2 provides an overview of the central theoretical developments in the field. Part 3 describes the empirical work on observing spreading processes in real-world networks. Finally, Part 4 goes into detail with recent and exciting new developments: dedicated studies designed to measure specific aspects of the spreading processes, often using randomized control trials to isolate the network effect from confounders, such as homophily. Each contribution is authored by leading experts in the field. This volume, though based on technical selections of the most important results on complex spreading, remains quite accessible to the newly interested. The main benefit to the reader is that the topics are carefully structured to take the novice to the level of expert on the topic of social spreading processes. This book will be of great importance to a wide field: from researchers in physics, computer science, and sociology to professionals in public policy and public health.
Complex networks appear across various contexts of our lives. Telecommunication, transport, infrastructure and finance are candidates to come to mind, and we humans ourselves, just going about our day as usual, meeting others, create a complex network of contacts. Also in our bodies, we can find intricate complex networks, not just of metabolic and molecular interactions, but in a structural sense. As a particular example, consider the human brain, where the cortex alone is built of 16 × 10^9 neurons, forming far-from-random structures. These networks can form a backbone on which spreading ...
This book provides the basis of a formal language and explores its possibilities in the characterization of multiplex networks. Armed with the formalism developed, the authors define structural metrics for multiplex networks. A methodology to generalize monoplex structural metrics to multiplex networks is also presented so that the reader will be able to generalize other metrics of interest in a systematic way. Therefore, this book will serve as a guide for the theoretical development of new multiplex metrics. Furthermore, this Brief describes the spectral properties of these networks in relation to concepts from algebraic graph theory and the theory of matrix polynomials. The text is rounded off by analyzing the different structural transitions present in multiplex systems as well as by a brief overview of some representative dynamical processes. Multiplex Networks will appeal to students, researchers, and professionals within the fields of network science, graph theory, and data science.
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 breakdown of standard theoretical frameworks and models. Until recently these systems were considered as haphazard sets of points and connections. Recent advances have generated a vigorous research effort in understanding the effect of complex connectivity patterns on dynamical phenomena. This book presents a comprehensive account of these effects. A vast number of systems, from the brain to ecosystems, power grids and the internet, can be represented as large complex networks. This book will interest graduate students and researchers in many disciplines, from physics and statistical mechanics to mathematical biology and information science. Its modular approach allows readers to readily access the sections of most interest to them, and complicated maths is avoided so the text can be easily followed by non-experts in the subject.
Spreading processes appear in diverse natural and technological systems, such as the spread of infectious diseases and the dissemination of information. It has been demonstrated that the structure of interaction among population members can dramatically influence spreading dynamics. Therefore, researchers have focused on studying spreading processes over complex networks, where interaction among individuals could be highly heterogeneous. This dissertation aims to add to the current understanding of networked spreading processes by investigating various aspects of the Susceptible-Infected-Susceptible (SIS) model. Our first contribution is related to the inverse problem of continuous time SIS spreading over a graph. In other words, we show the possibility of inferring the underlying network from observations on the node states through time. We formulate the inverse problem as a Bayesian inference problem and find the posterior probabilities for the existence of uncertain links. Second, we study the SIS spreading process over time dependent networks, where the contact network's links are not permanent. To analyze the effect of link durations on the epidemic threshold of the SIS process, we develop a temporal network model. In this model, the temporal links result from the transition of nodes between two auxiliary node states, namely active and inactive. Combining the dynamics of the network and the spreading process, we derive the mean-field equations that describe SIS spreading processes over such temporal networks. The analysis of these equations reveals the effect of link durations on the epidemic threshold in the SIS process. Third, we study the localization of epidemics in the SIS process. In general, the SIS model has an absorbing state where all individuals are healthy. However, depending on the infection rate value, this process can reach a metastable state, where the infection does not die out. In this metastable state, some parts of the network can be disproportionately infected. We quantify the infection dispersion in the network, and formulate a convex optimization problem to find an upper bound for the dispersion of infection in the network. Finally, we focus on the estimation of spreading data from partially available information. In general, various spreading-related functions are defined over the nodes of a network. Assuming access to the values of a function for a subset of the nodes, we use the concept of effective resistance distance and feed forward neural networks, to estimate the function for the remaining nodes. Although this dissertation focuses on the SIS model, the methods we have presented and developed here are applicable to a broad range of stochastic networked spreading processes. The exact mathematical treatment of such processes is intractable due to their exponential space size, and therefore there are still various unknown aspects of their behavior that require further work. Our studies in this dissertation advance the current knowledge about networked spreading models.
This book is the culmination of three years of research effort on a multidisciplinary project in which physicists, mathematicians, computer scientists and social scientists worked together to arrive at a unifying picture of complex networks. The contributed chapters form a reference for the various problems in data analysis visualization and modeling of complex networks.
Explores the emerging subject of epidemic dynamics on complex networks, including theories, methods, and real-world applications Throughout history epidemic diseases have presented a serious threat to human life, and in recent years the spread of infectious diseases such as dengue, malaria, HIV, and SARS has captured global attention; and in the modern technological age, the proliferation of virus attacks on the Internet highlights the emergent need for knowledge about modeling, analysis, and control in epidemic dynamics on complex networks. For advancement of techniques, it has become clear that more fundamental knowledge will be needed in mathematical and numerical context about how epidemic dynamical networks can be modelled, analyzed, and controlled. This book explores recent progress in these topics and looks at issues relating to various epidemic systems. Propagation Dynamics on Complex Networks covers most key topics in the field, and will provide a valuable resource for graduate students and researchers interested in network science and dynamical systems, and related interdisciplinary fields. Key Features: Includes a brief history of mathematical epidemiology and epidemic modeling on complex networks. Explores how information, opinion, and rumor spread via the Internet and social networks. Presents plausible models for propagation of SARS and avian influenza outbreaks, providing a reality check for otherwise abstract mathematical modeling. Considers various infectivity functions, including constant, piecewise-linear, saturated, and nonlinear cases. Examines information transmission on complex networks, and investigates the difference between information and epidemic spreading.
