Subsuming Complex Networks by Node Walks

The concept of node walk in graphs and complex networks has been addressed, consisting of one or more nodes that move into adjacent nodes, henceforth incorporating the respective connections. This type of dynamics is then applied to subsume complex networks. Three types of networks (Erd\'os- R\'eny, Barab\'asi-Albert, as well as a geometric model) are considered, while three node walks heuristics (uniformly random, largest degree, and smallest degree) are taken into account. Several interesting results are obtained and described, including the identification that the subsuming dynamics depend strongly on both the specific topology of the networks as well as the criteria controlling the node walks. The use of node walks as a model for studying the relationship between network topology and dynamics is motivated by this result. In addition, relatively high correlations between the initial node degree and the accumulated strength of the walking node were observed for some combinations of network types and dynamic rules, allowing some of the properties of the subsumption to be roughly predicted from the initial topology around the waking node which has been found, however, not to be enough for full determination of the subsumption dynamics. Another interesting result regards the quite distinct signatures (along the iterations) of walking node strengths obtained for the several considered combinations of network type and subsumption rules.