Element Level – Vertex Indices

One purpose of network analysis especially of social networks is to identify important actors, crucial links, subgroups, roles, network characteristics, and so on, to answer substantive questions about structures. There are three main levels of interest: the element, group, and network level. On the element level, one is interested in properties (both absolute and relative) of single actors, links, or incidences. Examples for this type of analyses are bottleneck identification and structural ranking of network items. On the group level, one is interested in classifying the elements of a network and properties of subnetworks. Examples are actor equivalence classes and cluster identification. Finally, on the network level, one is interested in properties of the overall network such as connectivity or balance. Algorithmic aspects concern the efficient computation of centrality indices, of groups and clusters, density, Clustering coefficient and transitivity. For this deliverable, algorithms for indices forming the basis of most studies were developed and implemented. A focus is on more efficient algorithms and robust and flexible implementations. In many experimental studies, network indices computed for real world data are compared with randomly generated graphs satisfying certain properties. As the networks under consideration are large, efficiency is again a crucial issue. Therefore, new efficient generators have been designed and implemented to create graphs according to popular stochastic models such as random graphs, small worlds, and evolving graphs with preferential attachment.