The Sociocast Hypergraph (On Social Mobility – Part II)

While graph theory has its roots in Euler’s Königsberg bridges, with a myriad of applications since then, its relationship to social networks has certainly been spotlighted by Zuckerberg’s Social Graph.

In its most basic form, a graph represents a set of entities and their relationships (for a great introduction to network theory, see Bradford Cross’ post about Network Theory). We refer to the entities nodes and the lines edges. In Facebook’s Social Graph, the nodes represent people and the edges represent the existence of friendship between them.

(Wikipedia)

Certainly, we can derive very interesting properties and patterns from simple graphs. We can study the centrality of individual entities, their prestige and importance, their connectivity. But to take our analysis further, we can relieve the simple graph of some of its innate limitations:

• Directed – we add direction to each edge, to model a flow phenomenon (i.e. influence). This means that the relationship between two individuals is not necessarily symmetric (think followers on Twitter).
• Weighted – we add a value to each edge which signifies the strength of the relationship. Not every influence relationship has the same intensity.
• Multiplex – we allow more than one edge between any two nodes, creating nodes that have multiple types of relationships with each other.
• Self-loops - we allow our individual nodes to connect to themselves, representing autonomy and self-influence.

While generalizing our notion of a simple graph adds complexity, it enables us to better model the reality in which individual behaviors take place.

This is the Sociocast Hypergraph, a directed, weighted, multi-relational, self-looped graph, where the edges represent the contexts (What does human mobility mean when it’s online? (On Social Mobility – Part I)) between individuals.