Overlapping social circles in historical elite networks - Using ‘k-circles’ as a minimal members decomposition approach

Jacob Aagaard Lunding, Anton Grau Larsen, Christoph Houman Christoph Houman Ellersgaard

Contact: agl.ioa@cbs.dk

This paper addresses the problems of missing network data, in particular from historical, biographical sources. This problem is particularly pertinent for graph theoretical approaches. However, we still have an ambition to identify key players and affiliations in weak structural data. We discuss the probable biases in missing data, arguing that these data presumably suffers from prominence bias, meaning both prominent individuals and their most prestigious or important affiliations are less likely to be omitted if those reporting the data has shared perceptions of prestige. To take these problems into account, we propose to move beyond graph theoretical measures based on path lengths when identifying central actors. Instead, looking at overlapping memberships in two mode networks is a more robust approach. We show that affiliation with overlapping members can be understood as ‘k-circles’, who like k-cores are k-degenerated graphs. Affiliations and actors are removed if they do not meet the minimal member overlap parameter Ω creating a set of densely connected affiliations and actors akin which matches ‘overlapping social circles’ akin to those described by C. Wright Mills in his studies of power elites. In our analysis, we first show the theoretical properties of a minimal k-circle graphs. Then using highly granulated data of more than 5,000 affiliations with around 55,000 positions held by 37,000 individuals, we show how k-circles can be applied to identify key affiliations and individuals in Danish elite networks and how changing the minimal member overlap parameter alters results. We compare the k-circle with coreness scores and the degree, closeness and betweenness centrality of individuals and affiliations in the one-mode projection of this graph. We then test the robustness of k-circles by simulating different types of missing data. We simulate three types of missing data based on prominence bias: 1) Missing low status individuals based on their network centrality or role in affiliations 2) The omission of positions in the network based on the centrality of the affiliation, the propensity of highly networked individuals to omit lower status positions and the different inclinations of diligence in reporting across individuals. 3) Missing data on low status or less formal affiliations. We finish by discussing the applicability of k-circles outside elite networks and historical biographical data on affiliation memberships.

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