Historical Network Research

This chapter introduces the field of historical network research. Many historical outcomes of interest to social scientists are greatly affected by network processes. These include revolutions, segregation, increasing inequality, party polarization, market development, state centralization, and the rise and fall of institutions. The chapter considers the current state of historical network research across these and other outcomes by focusing on six different network phenomena: cross-cutting ties, informal social ties, associational and organizational networks, narrative networks, cohesion, and brokerage and centrality. Extant research has presented some contradictory findings about the relationoship of these findings to major social outomes, suggesting further specification is necessary. The goal of this chapter is to provide a synthesis that illuminates a pathway to maximize future contributions.

Networks, Status, and Inequality

The notion that there is a single class of objects, “networks,” has been a great inspiration to new forms of structural thinking. Networks are considered to be a set of largely voluntary ties that often span organizational boundaries. Despite being divorced from formal hierarchies, they make possible other forms of differentiation, such as status. It is common for network data to be used to produce measures of the status of the nodes (individuals, organizations, cultural products, etc.) and the distribution of these statuses to describe a backdrop of inequality that may condition action or other processes. However, it is also important that network researchers understand the backdrop of various forms of potential inequality that may condition the collection of network data.

The Spatial Dimensions of Social Networks

The first law of geography holds that everything is related to everything else, but near things are more related than distant things, where distance refers to topographical space. If a first law of network science exists, it would similarly hold that everything is related to everything else, but near things are more related than distant things, but where distance refers to topological space. Frequently these two laws collide, together holding that everything is related to everything else, but topographically and topologically near things are more related than topographically and topologically distant things. The focus of the spatial study of social networks lies in exploring a series of questions embedded in this combined law of geography and networks. This chapter explores the questions that have been asked and the answers that have been offered at the intersection of geography and networks.

Networks

What is the role of social networks in driving persistent differences between races and genders in education and labor market outcomes? What is the role of homophily in such differences? Why is such homophily seen even if it ends up with negative consequences in terms of labor markets? This chapter discusses social network analysis from the perspective of economics. The chapter is organized around the theme of externalities: the effects that one’s behavior has on others’ welfare. Externalities underlie the interdependencies that make networks interesting to social scientists. This chapter discusses network formation, as well as interactions between people’s behaviors within a given network, and the implications in a variety of settings. Finally, the chapter highlights some empirical challenges inherent in the statistical analysis of network-based data.

Network Visualization

This chapter provides an overview of social network visualization. Network analysis encourages the visual display of complex information, but effective network diagrams, like other data visualizations, result from several best practices. After a brief history of network visualization, the chapter outlines several of those practices. It highlights the role that network visualizations play as heuristics for making sense of networked data and translating complicated social relationships, such as those that are dynamic, into more comprehensible structures. The goal in this chapter is to help identify the methods underlying network visualization with an eye toward helping users produce more effective figures.

Introduction

This chapter provides an introduction to this volume on social networks. It argues that social network analysis is greater than a method or data, but serves as a central paradigm for understanding social life. The chapter offers evidence of the influence of social network analysis with a bibliometric analysis of research on social networks. This analysis underscores how pervasive network analysis has become and highlights key theoretical and methodological concerns. It also introduces the sections of the volume broadly structured around theory, methods, broad conceptualizations like culture and temporality, and disciplinary contributions. The chapter concludes by discussing several promising new directions in the field of social network analysis.

Duality beyondPersons and Groups

This chapter focuses on the general principle of duality, which was originally introduced by Simmel as the intersection of social circles. In a seminal article, Breiger formalized Simmel’s idea, showing how two-mode types of network data can be transformed into one-mode networks. This formal translation proved to be fundamental for social network analysis, which no longer needed data on who interacted with whom but could work with other types of data. In turn, it also proved fundamental for the analysis of how the social is structured in general, as many relations are dual (e.g. persons and groups, authors and articles, organizations and practices), and are thus susceptible to an analysis according to duality principles. The chapter locates the concept of duality within past and present sociology. It also discusses the use of duality in the analysis of culture as well as in affiliation networks. It closes with recent developments and future directions.

An Introduction to Statistical Models for Networks

Network theoretical and analytic approaches have reached a new level of sophistication in this decade, accompanied by a rapid growth of interest in adopting these approaches in social science research generally. Of course, much social and behavioral science focuses on individuals, but there are often situations where the social environment—the social system—affects individual responses. In these circumstances, to treat individuals as isolated social atoms, a necessary assumption for the application of standard statistical analysis is simply incorrect. Network methods should be part of the theoretical and analytic arsenal available to sociologists. Our focus here will be on the exponential family of random graph distributions, p*, because of its inclusiveness. It includes conditional uniform distributions as special cases.

Three Perspectives on Centrality

This chapter presents three different perspectives on centrality. In part, the motivation is definitional: what counts as a centrality measure and what doesn’t? But the primary purpose is to lay out ways that centrality measures are similar and dissimilar and point to appropriate ways of interpreting different measures. The first perspective the chapter considers is the “walk structure participation” perspective. In this perspective, centrality measures indicate the extent and manner in which a node participates in the walk structure of a graph. A typology is presented that distinguishes measures based on dimensions such as (1) what kinds of walks are considered (e.g., geodesics, paths, trails, or unrestricted walks) and (2) whether the number of walks is counted or the length of walks is assessed, or both. The second perspective the chapter presents is the “induced centrality” perspective, which views a node’s centrality as its contribution to a specific graph invariant—typically some measure of the cohesiveness of the network. Induced centralities are computed by calculating the graph invariant, removing the node in question, and recalculating the graph invariant. The difference is the node’s centrality. The third perspective is the “flow outcomes” perspective. Here the chapter views centralities as estimators of node outcomes in some kind of propagation process. Generic node outcomes include how often a bit of something propagating passes through a node and the time until first arrival of something flowing. The latter perspective leads us to consider the merits of developing custom measures for different research settings versus using off-the-shelf measures that were not necessarily designed for the current purpose.

The International Trade Network

This chapter discusses key contributions social network analysis (SNA) has made to knowledge about the international trade network (ITN). The existing literature applies SNA to the ITN in three distinct directions. The first line of inquiry attempts to substantiate the hierarchical structure of the ITN envisioned by world system theory. The second line of inquiry describes the topological structure and evolution of the ITN. The third line of inquiry employs various modeling techniques to explain why the ITN takes place as observed. The existing literature largely builds upon the gravity model borrowed from international economics but makes some improvements. It also makes use of estimating methods developed for network data such as the multivariate regression quadratic assignment procedure. In future research, instead of relying on the gravity model, it is promising to directly use such SNA models as the exponential random graph model to explain the ITN.