Robustness of centrality measures against link weight quantization in social network analysis

Research on social network analysis has been actively pursued. In social network analysis, individuals are represented as nodes in a graph and social ties among them are represented as links, and the graph is therefore analyzed to provide an understanding of complex social phenomena that involve interactions among a large number of people. However, graphs used for social network analyses generally contain several errors since it is not easy to accurately and completely identify individuals in a society or social ties among them. For instance, unweighted graphs or graphs with quantized link weights are used for conventional social network analyses since the existence and strengths of social ties are generally known from the results of questionnaires. In this paper, we study, through simulations of graphs used for social network analyses, the effects of link weight quantization on the conventional centrality measures (degree, betweenness, closeness, and eigenvector centralities). Consequently, we show that (1) the effect of link weight quantization on the centrality measures are not significant to infer the most important node in the graph, (2) conversely, 5--8 quantization levels are necessary for determining both the most central node and broad-range node rankings, and (3) graphs with high skewness of their degree distribution and/or with high correlation between node degree and link weights are robust against link weight quantization.

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