Abstract

The idea of partitioning a network in terms of a specific conceptualization of equivalence has taken a powerful hold on the imagination of network analysts. Frequently, an empirically established blockmodel is assessed in terms of its consistency with a particular visualization of a network. We demonstrate that, while a visual representation of a network can be helpful, this also constrains powerfully our image of the structure of that network. This implies that a particular picture of a network is not sufficient for establishing the adequacy of a blockmodel. We argue that once committed to a specific form of equivalence, a network analyst must be committed also to an explicit method of assessing the extent to which a blockmodel is consistent with the selected form of equivalence. We provide a method for doing this. Additionally, and perhaps more importantly, efforts to measure the fit of a blockmodel in terms of a single form of equivalence reveal a serious weakness in the idea of using only a single for...

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