Can historians trust centrality? Historical network analysis and centrality metrics robustness

In this paper, we consider four measures of centrality (betweenness, closeness, degree, and eigenvalue centrality) in their use for the analysis of historical networks. Since the sources used by historians to construct such networks are by their nature incomplete and imperfect, it is necessary to consider as much as possible the robustness of these metrics, i.e., their stability with respect to the hazards that time has inflicted on historical documents. To study this, we apply a battery of tests to three networks constructed from medieval history data. The first is a political history network, which represents the links between protagonists of the conflict for the episcopal see of Cambrai in the 11^th century. The second is a network of socio-economic history, describing the credit relations of merchants in Ypres during the 13^th century. The third is a hagiographic network that depicts the connections between the lives of saints that are often compiled together in manuscripts. These tests are designed to simulate the processes of disappearance and degradation of the information contained in sources by imitating as closely as possible the situations that historians face when manipulating graphs. In each of them, we create a large set of new graphs by transforming the original graphs, then observing the effect of these transformations on the centrality metrics. For this, we use a random process, but one that respects the particularities of the considered networks, which are built from historical sources. Our results allow us to assess the general relevance of the use of centrality in historical network analysis, to compare the four metrics studied in terms of robustness, and to identify a set of methodological points to which the historian applying such techniques must pay particular attention.