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Mathematics LibreTexts

7: Connection

In this chapter we will examine some of the most obvious and least complex ideas of formal network analysis methods. Despite the simplicity of the ideas and definitions, there are good theoretical reasons (and some empirical evidence) to believe that these basic properties of social networks have very important consequences. For both individuals and for structures, one main question is connections. Typically, some actors have lots of connections, others have fewer. Some networks are well-connected or "cohesive", others are not. The extent to which individuals are connected to others, and the extent to which the network as a whole is integrated are two sides of the same coin.

  • 7.1: Networks and Actors
    Social network methods have a vocabulary for describing connectedness and distance that might initally seem rather formal and abstract. This is not surprising, as many of the ideas are taken directly from the mathematical theory of graphs. But it is worth the effort to deal with the jargon. The precision and rigor of the definitions allow us to communicate more clearly about important properties of social structures - and often lead to insights that we would not have with less formal approaches.
  • 7.2: Connection
    Since networks are defined by their actors and the connections among them, it is useful to begin our description of networks by examining these very simple properties. Focusing first on the network as a whole, one might be interested in the number of actors, the number of connections that are possible, and the number of connections that are actually present. Differences in the size of networks, and how connected the actors are tell us two things about human populations that are critical.
  • 7.3: Distance
    The distances among actors in a network may be an important macro-characteristic of the network as a whole. Where distances are great, it may take a long time for information to diffuse across a population. It may also be that some actors are quite unaware of, and influenced by others - even if they are technically reachable, the costs may be too high to conduct exchanges. The variability across the actors in the distances may be a basis for differentiation and even stratification.
  • 7.4: Summary
  • 7.E: Connection (Exercises)