Evolving Social Structures: Networks with People as the Edges

Abstract

Often social networks depict people as the nodes of the graph, with relationships among them as the edges. In this paper we will discuss networks in which social structures are represented as the nodes and the relationships, i.e., edges, between those structures are the individuals in the specific social context. Equally important is that we consider the social structures to be evolving structures, having implications on the characteristics of the overall network. Of course, the network as a whole also represents a social structure, but at a different level of granularity.

The characteristics of such networks only have humanistic salience in the context of specific human activities: only when applied in a human context. For this paper the primary motivating context will be the marriage structures in the early Mormon church. This dataset provides rich, evolutionary social structures: plural marriages, or marriage units, change over time as wives are married and divorced, children are born, and other members adopted.

While typical diagrams easily represent binary relationships, such as a marriage between individuals, linking children, adoptees, and other participants to marriages becomes difficult. Using hyperedges provides one solution to this problem: any number of nodes may be connected by one hyperedge relationship. However, these connections fail to fully express the intricacies of the social connection between those individuals. By capturing the social structures into evolving nodes, we can better examine those relationships on a micro level — intra-marriage changes, as well as the macro level — inter-marriage social interconnectedness of the community.

We use the term “evolving” to indicate that the node represents an identifiable social structure, e.g., a particular marriage, yet that structure is changing in non-trivial ways. Thus, there is an identity captured by the node that is maintained across various forms of human activity that affect important aspects of the represented structure. The resulting networks will have dynamic qualities that we anticipate to be representative of the progression of human activities in our motivating context.

We will present new visualizations of such networks of evolving socialstructures, by bringing together two concepts: chord (1) and Sankey (2) diagrams. Chord diagrams provide a detailed view of individual evolving structures, such as individual marriage units. Specifically, we can use this diagram to depict the state of a marriage at one particular point in time in a 2D representation that is then expanded to depict the evolving marriage structure from its conception to the death of all members. The Sankey diagram provides a method for joining the individual chord diagrams into a comprehensive social network: an identifiable marriage at each node with the edges between these nodes being the people that constitute the groups.

Individuals connect, in a directed flow, the marriage of their birth to their own marriage as an adult. We may therefore analyze this network for familial and ancestral structure in more intuitive ways. Patriarchal lineage can be followed as the flow from one patriarch through the marriage units by examining the male edges throughout the network.

1. D3 Chord Diagram Example: http://bl.ocks.org/mbostock/4062006, http://bost.ocks.org/mike/uberdata/; 2. D3 Sankey Diagram Example: http://bost.ocks.org/mike/sankey/