Course Introduction

How do we describe the large scale structure of social networks? In what sense are the architectures of new economy organizations different from their industrial era predecessors? If public health authorities want to minimize the danger of a viral epidemic, but have limited vaccinations, how should they be distributed throughout the population? But what if the public authority is the Federal Reserve and the feared epidemic is global financial contagion? Alternatively, if a marketing firm wants to initiate a word-of-mouth campaign for a new product, but can hand out free samples to only so many people, who should they pick?

These problems and many others in economics and sociology exhibit complex network structure, as specified by the pattern of interactions between actors or agents in a distributed system such as a friendship network, or a large firm, or even a national banking system. Although the study of social networks is a discipline with a 50 year history, the statistical analysis of large social and economic networks is only just becoming feasible, due to the recent, but rapidly increasing availability of large data sets and the computational capacity to analyze them. Furthermore, the subtle relationship between a system's interaction structure and its global behavior has been largely overlooked both by economics and sociology.

The primary aim of this course is to describe a unified theoretical framework for addressing network dynamics problems in the social sciences. A successful approach to this subject must necessarily be highly interdisciplinary, drawing upon techniques that are well established in physics, applied mathematics and computer science, but applied to the problems of sociology and economics.

Description

The course is designed to be an advanced undergraduate course. The material is drawn from graph theory, statistical physics, nonlinear dynamics, and computer science, as well as from social networks theory, and focuses on the empirical description of real networks, as well as sociologically relevant phenomena such as disease propagation, search, and the diffusion of innovations. It emphasizes a highly interdisciplinary approach to social science and draws heavily on the current research literature. As such, a number of mathematical ideas and techniques will be described and discussed, but at a conceptual rather than a methodological level. Although some training in mathematics may be helpful, it is not required. Instead, the course will rely heavily on notes prepared by the instructor that draw on the technical literature, but motivate and introduce the required concepts intuitively and, where possible, graphically. A full bibliography of the technical literature will be provided with the course notes, as optional reading for more advanced students.