Identifying Fragments in Networks for Structural Balance and Tracking the Levels of Balance Over Time

This paper presents three items. The first is a brief outline of structural balance oriented towards tracking the amount of balance (or imbalance) over time in signed networks. Often, the distribution of specific substructures within broader networks has great interest value. The second item is a brief outline of a procedure in Pajek for identifying fragments in networks. Identifying fragments (or patterns or motifs) in networks has general utility for social network analysis. The third item is the application of the notion of fragments to counting signed triples and signed 3-cycles in signed networks. Commands in Pajek are provided together with the use of Pajek project files for identifying fragments in general and signed fragments in particular. Our hope is that this will make an already available technique more widely recognized and used. Determining fragments need not be confined to signed networks although this was the primary application considered here.