Structures of social media networks provide a composite view of dyadic connectivity across social actors, which reveals the spread of local and global influences of those actors in the network. Although social media network is a construct inferred from online activities, an underlying feature is that the actors also possess physical locational characteristics. Using a unique dataset from Facebook that provides a snapshot of the complete enumeration of county-to-county connectivity in the USA (in April 2016), we exploit these two dimensions viz. online connectivity and geographic distance between the counties, to establish a mapping between the two. We document two major results. First, social connectivity wanes as physical distance increases between county-pairs, signifying gravity-like behaviour found in economic activities like trade and migration. Two, a geometric projection of the network on a lower-dimensional space allows us to quantify depth of the nodes in the network with a well-defined metric. Clustering of this projected network reveals that the counties belonging to the same cluster tend to exhibit geographic proximity, a finding we quantify with regression-based analysis as well. Thus, our analysis of the social media networks demonstrates a unique relationship between physical spatial clustering and node connectivity-based clustering. Our work provides a novel characterization of geometric distance in the study of social network analysis, linking abstract network topology with its statistical properties.