A complexity measure for military communication networks

Network complexity is one of the primary researches in the network science. There are a large number of research efforts concerned with the measuring of network (or graph) complexity, such as medium articulation (MAg), Offdiagonal Complexity (OdC), and so on. But they are difficult to describe the differences between military communication network (MCN) and other networks, since MCNs are man-made functional networks. According to the structure and functional characteristics of MCNs, we introduce the concept of military communication supernetwork (MCSN), adjacent matrix of supernetwork, type mixing matrix, type assortatively coefficient, and the definitions of supernetwork motif, core and the entropy of the motif. Then we take motifs which are the basic construct modules of MCSN, as the possible microstructure, and propose supernetwork motif entropy (SNME) as a complexity measure of MCNs. Finally, by taking the complexity measuring steps of a Naval Vessels Fleet communication supernetwork structure which was discussed in detail as an example, the computing results of SNME were compared with the present complexity measures, and it is demonstrated that SNME can measure the functional complexity of network when its structural complexity is determined.