Sunday, December 4, 2016

Note 17: Universal features vs. contextual interpretation

The last point already made the point that some edge weights representing real-world concepts such as probabilities or friendship do not allow a meaningful interpretation of graph theoretic distances. Such an interpretation is depending on the context, the meaning of the relationships and weights in the real-world. However, hip new "network science" was in part so very hot in contrast to lame, old "social network analysis", because it just applied any kind of measure to all kinds of complex networks to identify structures common to all of them. This was the case for Watts' and Strogatz' seminal paper on Small-Worlds (Watts, 1998) or for Barabási and Albert's paper on Scale-Free Networks (Barabási, 1999).

As one example, consider one of the data sets used by Watts and Strogatz, the neural network of a very small worm. In general, in a neural network, the interpretation of a small average graph theoretic distance in a contextually meaningful way is difficult. While one could say that it is a lower bound on the average number of firing events necessary to bring a signal from any one cell to any other cell, we know that the wiring of neural cells is so complex as to not allow all cells to talk to all other cells. However, in the new physics' way of looking at networks, the value did not have to `mean' anything much. They were looking at general patterns that would occur in all kinds of complex networks such as to identify universal laws of network generation.

For this goal, all kinds of network analytic measures can be applied to all kinds of network representation. However, without matching a network measure and the context of a research question, an interpretation is in general not possible.

Note 17. Applying network analytic measures to com-
plex networks in order to find universal structures does
not require a careful choice of the measure but also does
not lend itself to contextual interpretation. (Zweig, 2016)


 (Zweig2016) Katharina A. Zweig: Network Analysis Literacy, ISBN 978-3-7091-0740-9, Springer Vienna, 2016

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