What is a link? From a methodology standpoint, there is no answer to that question but only the recognition that when using graph theory and associated software tools, we project certain aspects of a dataset as nodes and others as links. In my last post, I “projected” authors from the air-l list as nodes and mail-reply relationships as links. In the example below, I still use authors as nodes but links are derived from a similarity measure of a statistical analysis of each poster’s mails. Here are two gephi graphs:

If you are interested in the technique, it’s a simple similarity measure based on the vector-space model and my amateur computer scientist’s PHP implementation can be found here. The fact that the two posters who changed their “from:” text have both of their accounts close together (can you find them?) is a good indication that the algorithm is not completely botched. The words floating on the links on the right graph are the words that confer the highest value to the similarity calculation, which means that it is a word that is relatively often used by both of the linked authors while being generally rare in the whole corpus. Elis Godard and Dana Boyd for example have both written on air-l about Ron Vietti, a pastor who (rightfully?) thinks the Internet is the devil and because very few other people mentioned the holy warrior, the word “vietti” is the highest value “binder” between the two.

What is important in networks that are the result of heavily iterative processing is that the algorithms used to create them are full of parameters and changing one of these parameters just little bit may (!) have larger repercussions. In the example above I actually calculate a similarity measure between each two nodes (60^2 / 2 results) but in order to make the graph somewhat readable I inserted a threshold that boils it down to 637 links. The missing measures are not taken into account in the physics simulation that produces the layout – although they may (!) be significant. I changed the parameter a couple of times to get the graph “right”, i.e. to find a good compromise between link density for simulation and readability. But look at what happens when I grow the threshold so than only the 100 strongest similarity measures survive:

First, a couple of nodes disconnect, two binary stars form around the “from:” changers and the large component becomes a lot looser. Second, Jeremy Hunsinger looses the highest PageRank to Chris Heidelberg. Hunsinger had more links when lower similarity scores were taken into account, but when things get rough in the network world, bonding is better than bridging. What is result and what is artifact?

Most advanced algorithmic techniques are riddled with such parameters and getting a “good” result not only implies fiddling around a lot (how do I clean the text corpus, what algorithms to look for what kind of structures or dynamics, what parameters, what type of representation, here again, what parameters, and so on…) but also having implicit ideas about what kind of result would be “plausible”. The back and forth with the “algorithmic microscope” is always floating against a backdrop of “domain knowledge” and this is one of the reasons why the idea of a science based purely on data analysis is positively absurd. I believe that the key challenge is to stay clear of methodological monoculture and to articulate different approaches together whenever possible.

Post filed under algorithms, epistemolgy, mathematics, network theory, social networks, statistics.

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