Categories and equivalences (redux)
To revisit a familiar argument: I find categorization to be a useful process, when engaged in exploratory analysis, if the categories themselves are up for grabs (and not just the assignments to those categories). For an example, the process of partitioning a network into sets of structurally-equivalent nodes -- those that share connections with the same others -- is an essential part of most network analyses. But the patterns of structural-equivalent sets are not always easy to interpret, as there isn't always a category label at hand with which I can make sense of the patterns found by the algorithm.
'Regular' equivalence causes me similar problems. Two actors are regularly equivalent if they have similar patterns of ties to equivalent others. A slightly abstruse definition, but an intuitive concept, given a proper exemple. Take a network describing communication behaviour within at least a medium-sized organization: you would expect to see certain patterns recurring within certain subsets - 'team leaders', 'technical managers', 'salesmen', etc. Some will match formal, appointed roles, but others will be categorising emergent niches in the structure. Many of these latter categorizations will not have clear given names. They may differ from equivalence-sets in networks from similar organizations, reflecting instead the peculiarities of the organization under study. Finding these and naming them -- as a categorization process -- I find to be hugely useful in getting under the skin of an organization.
In the past I've likened the process to early biology. This may be slightly grandiose (and certainly not original - see Morgan, 2006), but it's almost as if each new organization is a new ecosystem, full of new species. We can see some convergent evolution going on, but we shouldn't be blinded by expecting it.
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