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Collaboration social networks are traditionally modeled using graphs that capture pairwise relationships but have ambiguity between group collaborations and multiple pairwise collaborations. The authors present a new approach to analyzing collaboration networks using simplicial complexes to represent the co-authorship collaborations. They formally define several key novel metrics: higher dimensional analogs of vertex degree (e.g., simplex and facet degrees), homology, and minimal non-faces; and discuss their interpretation as it relates to co-authorship. They use these metrics in a study of an Army Research Lab dataset that includes the publications of the Communications & Networks Collaborative Technology Alliance.
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