Induction and deduction

Throughout this book we have been both inductive and deductive in our approach, with a strong bias in favor of being inductive when examining large networks. However, our uses of both induction and deduction were based on substance and driven by curiosity. For the three citation networks, induction reigned. When examining the social network citation networks, we wanted to learn the citation structure following two salient events. One was the formalization of centrality (and network centralization) in the Freeman (1977, 1979) papers. As we have noted, this triggered an explosion of work both extending and using these ideas. The other event was the recent interest of physicists in studying social networks. We stated rival expectations regarding the possible convergence or divergence of the traditional SNA and network science literatures. But, lacking anything beyond broad statements about this question in the literature, we had no foundation for a specific hypothesis.

This was just as well. One of our expectations was that the physicist conception regarding network science supplanted the SNA conception, especially regarding centrality. This was born out but, as noted in Chapter 4, this was not the end of the story. The full disciplinary sequence, for the centrality citation data ending in early 2013, was SNA ->• network science ->• neuroscience. We learned that the general concept of 'centrality' has multiple sources. There are parts of the broader centrality literature having nothing to do with traditional SNA concerns. Worries about 'the invasion of the physicists' may be a somewhat parochial conception within the older SNA community. This issue is explored more extensively in Chapter 4.

Our exploration of the patent citation network was inductive also. Given the four broad technological domains for 'utility patents' defined by USPTO and described in Section 5.1, we were curious about the flow of ideas between these broad technological areas as reflected by citations between patent applications and how they changed over time. Further, as technologies change over time, specific inventions are likely to have a limited shelf life. One crucial feature related to this is the lag between patents being granted and their ideas being picked up and used fruitfully for later inventions. Our interest centered on the distribution of these lags and their temporal dynamics.

Again, we were inductive in our approach to the Supreme Court citation network. However, there was an implicit hypothesis - about the line islands we identified having coherence -which underlay our analysis. Alternatively put, we gambled on this hypothesis being correct. If the gamble was lost, then this approach would be seen as severely flawed. Fortunately, thus far, every line island we have examined has a singular coherence even though the specific nature of their coherence differs by island. Establishing the presence of coherence of decisions being co-cited frequently was a purely inductive, but not surprising, outcome. This coherence among a set of frequently co-cited decisions comes either from the constitutional principles underlying these sets of decisions, the substantive domains of the decisions, or both. Induction of a different sort followed the identification of coherent patches in this citation network. Having identified them, we sought to understand both the decisions and the citations between them in their historical, social, and political contexts. Beyond the line islands considered in Chapter 6, two we considered were technologically driven. One concerned rail raids when rail was an emerging technology with great commercial and social implications. Another featured maritime law, first defined over centuries for travel on seas and oceans, and then adapted as internal waterways - rivers and lakes - were used in the USA, especially for commerce.

For the football network, our approach was completely deductive. Based on our reading of the literature regarding football player moves, we formulated an explicit set of hypotheses. We knew that players move in the hope of advancing their careers, while clubs recruited players with the intent of achieving greater success (or avoiding failure) on the field. Coupling the decisions of players and the decisions of clubs is a highly uncertain processes for reasons outlined in Chapter 7. We state 21 hypotheses in Chapter 7 and test them. The results of these tests are reported in Chapters 7 and 8. While some hypotheses were obvious, others were counter to conventional thinking about player movements. Many hypotheses passed muster, some failed miserably, and others, while sounding plausible, turned out to be untestable in the sense of there being both supporting and refuting evidence about them. Not surprisingly, regarding the failed hypotheses and the untestable hypotheses, conventional wisdom about football in England does tend to be supported by selective attention to the evidence.

In essence, we returned to induction for our analysis of the large US spatial network. Indeed, we state no hypotheses. Our intent was to combine two broad- seemingly incompatible-approaches to mapping spatial diversity. The resulting compromise led to results sitting between these two broad approaches. Of course, this does not have surprise value because we were more attentive to both network geography (adjacency in space) and also appropriate statistical data. As a result, our results provide the foundations for a deeper characterization of the spatial distribution of diversity in the USA.

The final chapter provides a partial summary of the results provided in Chapters 4-9, together with commentary on the utility of the methods used throughout this book. Also proposed in the final chapter are some suggestions for further work. Despite all that is accomplished here, one salutary implication is that much more needs to be done. Pursuing these issues has immense appeal.

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