B0830
Title: Exploring and modelling multigraphs
Authors: Termeh Shafie - University of Konstanz (Germany) [presenting]
Abstract: A multigraph approach to analyse networks with multiple edges and edge loops is introduced. Multigraph data structure is described with examples of their natural appearance, together with a description of the possibility to obtain multigraphs using blocking, aggregation and scaling. A novel way of representing multigraphs using edge multiplicities is presented and graph complexity is quantified by the distribution of edge multiplicities. Using this representation, a random multigraph model based on independent edge assignments (IEA) to sites of vertex pair is given and several complexity statistics under IEA are derived. It is described how these statistics can be used to analyse local and global network properties and to convey structural dependencies in social networks. Further, some natural extensions to this approach are presented including (i) an alternative random multigraph model called random stub matching (RSM) which is a special kind of preferential attachment model, (ii) information theoretic tools that may be used to explore interdependencies among network variables, and (iii) an application of these tools to select general exponential random graph models.
