PolySocial Networks (PoSN)
THIS MATERIAL ©1978–2016 SALLY A. APPLIN AND MICHAEL D. FISCHER. ALL RIGHTS RESERVED.
PolySocial Networks (PoSN) are the abstract networks representing the union of all instantiable networks for each person in an aggregate. The instantiation of a subset of these in a given context we call PolySocial Reality (PoSR). Each person in the network possesses a perspectual intersection of many potential resources for information and interaction, only some of which can be instantiated in a given instance, considering constraints of time, cognitive capacity, and mutual exclusion.
Multigraphs support one of the aspects of PoSN/PoSR: the multiplicity of different relations that may underly multiple intersecting social networks. Gjoka, et al (2011) propose a promising approach to this problem based on multigraphs: graphs whose vertices may be connected by more than one edge. Because of the multiplicity of edges, each type representing a different context for social relations, a projected multigraph will be more likely to have a higher degree of connectivity. (See Fig. 1)
Fig. 1. Multigraph integrating two networks.
Combining multigraphs with metagraphs (Basu and Blanning, 1992) appears a reasonable initial mathematical representation for an exploration of PoSR through the analysis of trails and aggregated trails. A metagraph is a graph where vertices are sets, and edges are connections between sets (see Fig. 2). A multigraph that is also a metagraph permits us, at least, to represent the data in a form that is interoperative and can be converted into different forms such as matricies, XML or relational data suitable for online analytic tools for which a range of algorithms for methods of analysis have been established.
Fig. 2. Multi-Metagraph.