Embedding vertex intrinsic relevance in network analysis: the case of Betweenness. (arXiv:1905.03300v1 [cs.SI])

Complex network theory (CNT) is an expanding science whose basis are the concepts of graph theory. CNT deals with analyzing networked systems considering vertex exchanging information by means of edges, eventually considering connections strength using weights. The importance of a vertex is determined by its degree, position in the network and connections strength. Therefore, all the vertices have the same intrinsic relevance in the network and the connectivity studies attribute the relevance. Nevertheless, the identical relevance assumption does not allow analyzing systems where some vertices represent strategic physical locations (e.g. hospitals, administrative building, schools, water and energy sources, etc.) or representative persons (e.g. presidents, prime ministers, intellectuals, etc.) for which the relevance cannot be derived from the connectivity network structure without embedding the information about the vertex intrinsic relevance. Therefore, the aim of this effort is expanding CNT tools to analyze networked systems introducing the vertex intrinsic relevance. As example the embedding in the Betweenness the vertex intrinsic relevance will be used. The Florence family network and a simple supply network will allow showing and discussing the increasing of CNT analysis features.

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