Temporal and spatial networks

Our primary concern is understanding both large temporal and large spatial networks in ways going beyond simple general descriptions of their structures. For the former, doing this amounts to discerning the structure(s) of such networks as they develop over time, and grasping the social forces driving these changes. For the latter, it involves understanding spatial social patterns and the processes by which they were generated. For both network types, these two broad tasks - delineating structures and understanding their formation -go hand in hand: doing one without the other leaves our understanding of these networks incomplete. However, in order to understand the impact of social forces, it is necessary to know the structure(s) of networks. We focus, initially, on outlining foundational network concepts in Chapter 2. A detailed presentation of methods for analyzing citation networks is included in Chapter 3. In the remaining chapters, we study how temporal networks change and social phenomena are distributed over spatial networks. We provide substantively based interpretations of the results we obtain. As is usually the case, for us, creating these understandings was an iterative process where empirical results led to substantive understandings which, in turn, triggered further analyses. We report results of these analytic sequences but without reporting the iterations.

Modern social network analysis

Freeman (2004) argued that four features define modern social network analysis (SNA). In a slightly expanded form they are:

1. SNA is founded on a 'structural intuition' regarding social ties linking social actors. This motivates the study of the social networks formed by these social ties when they form coherent wholes.

2. 'It is grounded in systematic empirical data (emphasis added).' Implicitly, network data must be meaningful for studying social networks: not all social network data sets are useful.

3. 'It draws heavily on graphical imagery' to represent these social networks and their salient features in useful ways. Visualization of these features is useful both for displaying results and for suggesting further avenues of inquiry.

4. 'It relies on the use of mathematical and/or computational models.' This dual reliance has grown even stronger since 2004.

We add the following three items:

1. Fully understanding social networks in time and across space requires a concern with substance.

2. When studying the operation of social processes creating, sustaining, and dissolving social networks, Doreian and Stokman (1997), the relevant network data must be temporal. Intuitively, a temporal network has units and relational ties distributed through time.

3. Given that most social networks are conditioned by the contexts within which they exist, ignoring these contexts imposes major constraints on understanding network phenomena. One contextual feature is the geographic space within which these networks are located. Spatial networks have units and relational ties distributed across geographical space.

While substance can never be ignored safely, we note that many networks have been studied without considering time. Other networks were studied while ignoring space. Quite often, neither time nor space had relevance for analyzing network data. This has changed dramatically in recent years with considerable attention being devoted to both space and time when studying social networks. Consistent with this new emphasis, the networks we consider here involve time or involve space and, occasionally, both. In the main, we focus on temporal networks.

Building upon the above seven items, our study of temporal networks and spatial networks is informed by four working assumptions:

1. Social networks form through the operation of social processes. These processes have direct relevance for studying networks, implying that substantive ideas really matter. In turn, the contexts within which social networks are generated are crucial for understanding network creation and the consequences they have for the people, groups, organizations, states, and nations located in them.

2. As Freeman noted, computation has been crucial. However, practical and sound computational methods are required for detecting useful structural patterns in networks. Developing these methods is necessary, even mandatory. Ideally, computational methods are informed by substantive concerns. However, we have no objection to developing methods for their own sake. Even so, the use of methods developed in this fashion requires some justification in terms of both substance and relevance, at least as far as understanding social network processes is concerned. Methods are more useful when coupled to the substantive issues for which analyses are performed.

3. Temporal network data have to be meaningful in terms of both social substance and social contexts. This implies that temporal network data need to be selected carefully in order to be relevant substantively. The same arguments hold for spatial networks.

4. Coupling substance, context, methods, and data is most effective when these items are combined into a single coherent framework.

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