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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. We present a new approach to analyzing collaboration networks using simplicial complexes to represent the co-authorship collaborations. We formally define several key novel metrics: 1) higher dimensional analogs of vertex degree (e.g., simplex and facet degrees), 2) homology, and 3) minimal non-faces; and discuss their interpretation as it relates to co-authorship. We use these metrics in a study of an Army Research Lab dataset that includes the publications of the Communications & Networks Collaborative Technology Alliance. In particular, our study reveals many properties of large networks mirrored by this single-program publication dataset: the distinction of certain simplex degrees from vertex degrees, a power law characteristic in facet degrees, and some properties of topological “holes” and minimal non-faces.