# Methods, techniques, and algorithms

The formal core of the book is contained in Chapters 2 and 3, where we presented two broad sets of ideas: 1) foundations with network analytic concepts, and 2) a coherent framework for analyzing temporal networks. Methods used in multiple chapters were presented there. Additional formal tools and methods were presented in Chapter 9 for the analysis of spatial networks.

We do have a particular fondness for a set of methods, a fondness that may have shown throughout the book. We mention them here. Given the historical origins of main path analysis, we like this method because it answers a particular set of questions well. However, our results showed it to be quite limited. Another very useful method is the establishment of islands, particularly line islands, a method used for studying all of the citation networks. While it is useful for delineating coherent parts of networks, we show that there are other methods that can be used for similar purposes. Clustering symbolic data had great value for studying both the patent citation network and a quite different problem relating to the football data. Finally, clustering with a relational constraint was crucial for the analysis of the large spatial network we considered.

While network analytic techniques are considered often as highly portable, and therefore are assumed to be relevant for all networks, we have considerable skepticism on that front as well. In part, this is driven by having to think about substance, substantive issues, and the appropriateness (or not) of specific techniques for seeking substantive understandings of empirical phenomena. In short, we do not think there are cookie cutter methods applicable to every network problem. Not every problem can be solved by using a hammer!

We think there are two potentially troublesome - at least for us - trends in contemporary network analysis. One is the presumption of universal portability, with attempts to use any technique simply because it happens to be in fashion. One example that we encountered took the form of trying to fit a scale-free distribution, developed usefully for a class of large networks, to the degree distributions of very small networks, despite such a usage making no sense. The second is the presumption that 'my method' is the best of all methods. While this is a choice each researcher can make, it often comes with attempts to enforce an orthodoxy regarding how networks 'should' be analyzed. These two strands of thought strike us as unproductive, and so we resist them.

In large part, this resistance stems also from realizing the importance of matching substance with methods in the pursuit of understanding. The tools we used were coupled in ways we thought appropriate for the substantive issues engaging our interest. While they worked well for us, we are not claiming they are the only useful tools. Nor do we claim that we could have obtained our results only be using them. Other tools could be equally useful, perhaps even better for our purposes, and our hope is that different tools provide complementary results and insights for understanding social phenomena. If so, it seems best to couple them rather than confine attention to one, and only one, set of preferred tools.

Another relevant motivation for the book stemmed from the need for fast, efficient algorithms that are practical for analyzing large networks. Without such new algorithms, none of what we have done would have been possible. Most of the algorithms supporting the methods for which we have great fondness were programmed with efficiency as a primary design criterion.

During our partial survey of other approaches to large networks in totally different areas, we were struck by how they were designed with specific substantive problems in mind. No doubt, they are also portable, but it does not follow that they must be used to study the kinds of networks we considered, nor that the methods we have developed and used are appropriate for other substantive domains. Portability is fine and we greatly like to see ideas flowing between diverse areas. However, neither the blind importation of methods nor the attempt to enforce an unthinking orthodoxy have any appeal. Matching of methods to substantive problems is crucial. Given this, we do think that some of the methods we surveyed from other domains will have great value when adapted for studying social network analytic problems and we plan to include them in future work.

The methods we used throughout this book for network analyses were programmed as integral parts of Pajek. As we noted earlier, Pajek served our purposes very well, especially for large networks. Of course, we hope that our efforts were persuasive regarding this. Despite our commitment to Pajek, we have no interest in claiming that it is the only relevant program for studying large networks. Again, combining results from using different methods implemented in diverse programs has great merit.