We present fully dynamic algorithms for maintaining betweenness centrality (BC) of vertices in a directed graph G = (V,E) with positive edge weights. BC is a widely used parameter in the analysis of large complex networks. We achieve an amortized O(ν∗ · log n) time per update with our basic algorithm, and O(ν∗ · log n) time with a more complex algorithm, where n = |V |, and ν∗ bounds the number...

In this paper, the relationship between the network synchronizability and the edge distribution of its associated graph is investigated. First, it is shown that adding one edge to a cycle definitely decreases the network sychronizability. Then, since sometimes the synchronizability can be enhanced by changing the network structure, the question of whether the networks with more edges are easier...

Estimating the importance or centrality of the nodes in large networks has recently attracted increased interest. Betweenness is one of the most important centrality indices, which basically counts the number of shortest paths going through a node. Betweenness has been used in diverse applications, e.g., social network analysis or route planning. Since exact computation is prohibitive for large...

Egocentric centrality measures (for data on a node’s first-order zone) parallel to Freeman’s [Social Networks 1 (1979) 215] centrality measures for complete (sociocentric) network data are considered. Degree-based centrality is in principle identical for egocentric and sociocentric network data. A closeness measure is uninformative for egocentric data, since all geodesic distances from ego to o...

This paper aims to identify central points in road networks considering traffic demand. This is made with a variation of betweenness centrality. In this variation, the graph that corresponds to the road network is weighted according to the number of routes generated by the traffic demand. To test the proposed approach three networks have been created, which are Porto Alegre and Sioux Falls citi...

Estimating influential nodes in large scale networks including but not limited to social networks, biological networks, communication networks, emerging smart grids etc. is a topic of fundamental interest. To understand influences of nodes in a network, a classical metric is centrality within which there are multiple specific instances including degree centrality, closeness centrality, betweenn...

The betweenness centrality of a vertex of a graph is the portion of shortest paths between all pairs of vertices passing through that vertex. We study selected general properties of this invariant and its relations to distance parameters (diameter, mean distance); also, there are studied properties of graphs whose vertices have the same value of betweenness centrality.