Structure and Dynamics of Information in Networks

Preface The present notes are derived from a course taught at the University of Southern California. The focus of the course is on the mathematical and algorithmic theory underpinning the connections between networks and information. These connections take two predominant forms: • Network structure itself encodes a lot of information. For instance, friendships between individuals let us draw inferences about shared interests or other attributes (location, gender, etc.). Similarly, hyperlinks between documents indicate similar topics, but can also be interested as endorsements, and thus hint at quality. The list of scenarios in which network structure helps us interpret information about individual nodes continues beyond this list, and will be explored in more detail throughout these notes. • Networks also play a crucial role in disseminating or gathering information. This applies both to social networks, in which communication between individuals happens naturally, and computer networks, which are designed explicitly to facilitate the exchange of information and distributed computations. We will draw analogies between the two types of networks, and investigate the mathematical underpinnings of the diffusion of information over networks in the later chapters of these notes. These notes are designed to accompany a one-semester graduate-level course in computer science. We assume a solid mathematical background, and familiarity with basic algorithmic techniques, including flows and cuts; the necessary topics are covered in textbooks by Kleinberg and Tardos [222] and Cormen et al. [101]. In particular, we will assume familiarity with Linear Programming (see, e.g., [88, 201]) and the concept of approximation algorithms [179, 329], as well as with basic notions of randomization in algorithms [258, 266]. A basic understanding of graph theory is also required (see, e.g., [50, 116]). Several recent books cover topics overlapping with the content of these notes. " The Structure and Dynamics of Networks " [277] by Newman, Barabási and Watts collects a number of recent papers on network analysis and epidemic processes on networks, predominantly with a physics bent in the type of analysis. The collection " Network Analysis " edited by Brandes and Erlebach [62] covers many of the algorithmic and mathematical foundations of static network analysis. The recent book " Social and Economic Networks " [190] by Matthew Jackson covers several of the same problems studied here, in particular the diffusion of innovations and modeling and properties of networks. Its focus tends to be on essentially uniformly random models of networks, and mean-field approximations …