Centrality indices assign values to the vertices of a graph such that vertices with higher values are considered more central. Triggered by a recent result on the preservation of the vicinal preorder in rankings obtained from common centrality indices, we review and extend notions of domination among vertices. These may serve as building blocks for new concepts of centrality that extend more di...

The analysis of biological networks involves the evaluation of the vertices within the connection structure of the network. To support this analysis we discuss five centrality measures and demonstrate their applicability on two example networks, a protein-protein-interaction network and a transcriptional regulation network. We show that all five centrality measures result in different valuation...

Centrality measures, erstwhile popular amongst the sociologists and psychologists, has seen wide and increasing applications across several disciplines of late. In conjunction with the big data problems there came the need to analyze big networks and in this connection, centrality measures became of great interest to the community of mathematicians, computer scientists and physicists. While it ...

PageRank centrality is used by Google for ranking web-pages to present search result for a user query. Here, we have shown that PageRank value of a vertex also depends on its intrinsic, nonnetwork contribution. If the intrinsic, non-network contributions of the vertices are proportional to their degrees or zeros, then their PageRank centralities become proportion to their degrees. Some simulati...

In this paper, we revisit the concept of (normalized) closeness centrality a vertex in graph and investigate it some graphs under operations. Specifically, derive formulas that compute vertices shadow graph, complementary prism, edge corona, disjunction graphs.

We present BigSparse, a fully external graph analytics system that picks up where semi-external systems like FlashGraph and X-Stream, which only store vertex data in memory, left off. BigSparse stores both edge and vertex data in an array of SSDs and avoids random updates to the vertex data, by first logging the vertex updates and then sorting the log to sequentialize accesses to the SSDs. This...

Centrality measures provide a means to differentiate the importance of vertices in a network. These measures are mathematically clear, but the algorithms to compute them often have quadratic time complexity or worse. This may lead to significant computational challenges when applied to large networks. In this paper, we propose a local strategy for three frequently used centrality measures: (i) ...

In a social network individuals have prominent centrality if they are intermediaries between the communication of others. The betweenness centrality of a vertex measures the number of intersecting geodesics between two other vertices. Formally, the betweenness centrality of a vertex v is the ratio of the number of shortest paths between two other vertices u and w which contain v to the total nu...