Where do networks come from? Numerous theories direct us to the causes of networks (e.g., homophily, triadic closure, physical proximity), some emphasizing outside factors (exogenous causes) and others emphasizing point-in-time network structure (endogenous causes) as shaping a network’s future trajectory. So far, we have examined such causal theories using cross-sectional snapshots in the form of metrics (centrality, density), partitions (clusters), and maps or spaces (visualization). These approaches generally suffer from a lack of stochastic features and observational overdetermination: for example, we observe a pattern in a given school on a given day, but that pattern could result from actor preferences and constraints in the setting. Disentangling such effects requires an inferential approach to probabilistically examine various effects. To the extent that we want to identify causal forces shaping the networks, understanding the unfolding of relations in time – how the individual ties in a network (the dyads joined by one or more relations) and the entire structure of these relations emerge and evolve – is crucial for testing network theories.

Is culture the glue that holds the social structures of society together? Or are there “culture wars” that fundamentally divide us? Clearly, the answer is somewhere in the middle, and trying to understand precisely how culture and social structure interrelate to unite or divide remains a core sociological endeavor. Social network analysis alone cannot resolve such an enormous puzzle, but its methods provide important tools for formalizing a jointly structural and cultural approach to studying society. In this chapter, we conclude Part II on Seeing Structure by outlining efforts to see dualities in the connections between structure and culture – that is, to study how enduring patterns of interaction interrelate with shared understandings, tastes, meanings, and other attitudinal measures. We also discuss the structural analysis of meanings themselves and the application of social network techniques to cultural phenomena.

When does a collection of individuals become a group or a community? What holds groups, communities, and societies together, even as individuals come and go? These questions concern social cohesion, the bonds through which otherwise disconnected individuals become part of something larger and more lasting than themselves. Social cohesion is perhaps the most central issue in the founding of sociology as a discipline, and its relevance persists today. Social network analysis has much to offer in making the study of social cohesion more formal and precise. Whereas in the previous chapter, we examined structures from the standpoint of their constituent elements of dyads and triads, here we step back to try to see more of the bigger structural picture through the overall pattern of ties in a network.

Whereas in one-mode data, individuals or groups are connected directly with one another through interactions or relations, in two-mode data, individuals are indirectly connected with one another through affiliations (events, organizations, associations, alliances, and so on). Affiliation data are often used as a proxy for detecting ties among social actors when direct evidence of ties is difficult to obtain. For example, it is generally easier to know that two people belong to the same club or work in the same department than to know that they have lunch together every Thursday. But affiliation data can also be used to see aspects of social structures not visible in one-mode networks. Duality is a kind of structural relation that shows how levels of social structure intersect with one another. We discuss the classic approach to duality as well as two generalizations that extend the duality approach in hierarchical, temporal, and spatial directions.

Connectionist approaches to social networks often speak of flows of ideas, attitudes, and behaviors through ties as social influence and as peer influence in the specific case of flows among friends and acquaintanceships. Modeling social influence is no easy task. How do we determine where a particular idea came from in a network and who influenced whom? In establishing the presence of social influence, a researcher must theoretically and empirically address many potentially confounding factors and alternate explanations. In the previous chapter, we covered network approaches to generic flows at scale. In this chapter, we more thoroughly cover some of the thorny issues involved in tracing interpersonal influences and key modeling strategies in obtaining more detailed views of what flows and to whom.

Images can be powerful; and, as the saying goes, “with great power comes great responsibility.” Today, the world is suffused with images through various media, and people have come to expect pictures to tell them stories. With increased computational power, images of quantitative data are increasingly part of the “stories” one commonly sees and are powerful in communicating research findings. Many of these images are informative and effective; others are confusing, convey little actual information, or, sadly, are used to intentionally mislead for ideological reasons. Network science has always used compelling images to tell stories about structures, and the field is therefore particularly suited to make the most use of this era of data visualization. But given the vastly expanded palette of visualization available today, how does the researcher decide what is a good network image?

Having lived through a global pandemic, or more trivially, having seen online memes “go viral,” we are all intuitively familiar with the spread of things through network ties. Diseases, memes, used books, and cash are ready examples of things passed from one person to another. Somewhat less familiar, perhaps, is that a fundamentally similar mechanism underlies many of our social behaviors. Understanding such processes is therefore related to understanding how anything – information, rumors, diseases, and so on – diffuses through a system. Key questions include: How does a network structure as a whole (its topology) affect the diffusion process? And how does a node’s position in this structure affect the likelihood of transmitting and receiving flows?

The primary aim of social network analysis is building and evaluating theories of social structure – that is, enduring patterns of human interaction and ways of thinking about and organizing human groups. The sheer complexity of social structure prevents encapsulation in any single model, and this complexity is compounded as we incorporate cultural beliefs and social expectations in addition to interactions. Networks link actors to one another in systems, raising tricky questions about the locus of control and activity, particularly regarding the extent to which people are active agents or passive puppets (to put it bluntly) of social structure. While acknowledging deep and ultimately unsettled issues in the field, we provide readers with an overarching though still evolving theoretical account of social structure that can guide both inductive and deductive social network research and allow plug-in points for different perspectives on agency, culture, and constraint.

The frontiers of network analysis keep expanding with new data sources and new ways to see structure and model relations. Traces of interactions and relations are now constantly streaming and being recorded through social network platforms. New technologies are affording new ways to visualize and analyze massive online data sets, as well as flowing interactions using video and sensor data. These new data sources are being met with new data mining approaches, giving us a deeper and wider view of social structure. Moreover, these new technologies are undoubtedly changing aspects of social structure itself, as people form ties and influence one another in ways that were unimaginable a generation ago. What is missing, we contend, is a systematic way of linking these projects to a theory of social structure (as outlined in Chapter 2). We conclude by proposing three strategies for addressing open problems and moving forward in modeling social structure.

Stop. Take a moment to look around. What do you see? No matter where you are, you are likely perceiving a world consisting of things. Maybe you are reading this book in a coffee shop, and if so, you probably see people, cups, books, chairs, and so on. You see a world of objects with properties, yourself included: white cups are on wooden tables, people sitting in chairs are reading books and talking with one another. At the same time, you are a subject, responding to this world and actively bringing yourself and these objects into interrelation. And yet, the world of objects with properties that you are perceiving is but one slice of a complex reality.

Whereas previous chapters have focused on networks as conduits through which important resources and influences flow, this chapter provides a more in-depth account of the positional approach to networks. In doing so, we move away from conceptualizing social structures as more or less cohesive and integrated groups, cliques, communities, etc., toward a view of social structures as comprised of role structures. To use the baseball analogy, in moving toward a more positional view of networks, we shift from seeing teams as interacting individual players with relations with one another to seeing players as enacting the game through an interrelated set of positions on the field that come with role expectations. Thus, as depicted in our view of social structure in Figure 2.3, we begin to move upward and to the right – that is, toward higher levels of structure and greater levels of conceptual abstraction. Doing so requires a different set of methods, which we introduce in this chapter.

Some people take orders all day. Others give them. And most people are somewhere in the middle. While relations of “who orders whom” are generally established through formalized hierarchies of authority, informal relations such as business partnerships and even friendships are also frequently hierarchical in some way: some business partners have more control over important resources, some friends have more clout. Indeed, status and reputation structure almost all areas of social life. To understand social structure, we must attend to both horizontal relations in which individuals are connected through frequently mutual feelings of belonging, as well as vertical relations of power, authority, deference, and status that are asymmetric. Ultimately, how community and hierarchy combine is one of the most vexing concerns in the social sciences. Building on the previous chapter’s focus on groups and cohesion, this chapter focuses on aspects of social structures that are more asymmetric, centralized, or hierarchical.