Motifs in weighted networks and their Hirsch subgraphs

Motifs are patterns of interactions occurring in complex networks and characterized by the fact that they occur significantly more than expected. Network indicators derived from motifs are introduced in this contribution. They provide yet another numerical view on network structures. Based on the notion of a motif’s h-index the motif’s Hirsch subgraph is constructed. This subgraph is a new characteristic structure in weighted networks. Use of these notions has been illustrated in two case studies: one involving a co-authorship and one involving a co-keyword network.