Metrics for characterizing network structure and node importance in Spatial Social Networks

Social Network Analysis offers powerful tools to analyze the structure of relationships between a set of people. However, the addition of spatial information poses new challenges, as nodes are embedded simultaneously in network space and Euclidean space. While nearby nodes may not form social ties, ties may exist at a distance, a configuration ill-suited for traditional spatial metrics that assume adjacent objects are related. As such, there are relatively few metrics to describe these nuanced situations. We advance the burgeoning field of spatial social network analysis by introducing a set of new metrics. Specifically, we introduce the spatial social network schema, tuning parameter and the flattening ratio, each of which leverages the notion of distance' to augment insights obtained by relying on topology alone. These methods are used to answer the questions: What is the social and spatial structure of the network? Who are the key individuals at different spatial scales? We use two synthetic networks with properties mimicking the ones reported in the literature as validation datasets and a case study of employer-employee network. The methods characterize the employer-employee as spatially loose with predominantly local connections and identify key individuals responsible for keeping the network connected at different spatial scales.