EXPONENTIAL RANDOM GRAPH MODELS FOR MINERAL NETWORK DATA

A new approach to mineralogy is to represent the distribution of minerals in rocks and ore deposits by mineral network diagrams. One of the first renderings of mineral network data was given in [1], where minerals were represented by nodes and two minerals were connected by an edge if they were found at the same location. Data-driven discovery and visualization techniques from open access sources were used to uncover coexistence patterns among hundreds of mineral species and their localities.

In this talk we consider the statistical modeling of mineral network data. In particular, we formulate an exponential random graph model for mineral networks that is able to model the complex dependence structures of network graphs. The model simultaneously allows the systematic study of features such as the node degree distribution, connected subgraphs, clustering, centrality, and other network structures. The goal is to employ the model to discover patterns of mineral formation, distribution, diversity, and coexistence of minerals. In addition, the model will pinpoint which mineral attributes are significant for mineral species coexistence.

1. Morrison SM, Liu C, Eleish A, Prabhu A, Li C, Ralph J, Downs RT, Golden JJ, Fox P, Hummer DR, Meyer MB, Hazen RM (2017) Network analysis of mineralogical systems. American Mineralogist 102:1588-1596