Finding key vertices in large graphs is an important problem in many applications such as social networks, bioinformatics, and distribution networks. Betweenness centrality is a popular algorithm for finding such vertices and has been studied extensively, yielding several parallel formulations suitable to supercomputers and clusters. In this paper we implement and study betweenness centrality i...

This study examines whether or not the positions of the network affect firm performance. A sample set involves 35 firms in the semiconductor industry, including four main subsidiary industries: fables, IC manufacturing, packaging and testing. Different from previous research, this study tests relational measurement and firm performance. We collected patent citation data to represent diverse org...

Traumatic brain injury affects brain connectivity by producing traumatic axonal injury. This disrupts the function of large-scale networks that support cognition. The best way to describe this relationship is unclear, but one elegant approach is to view networks as graphs. Brain regions become nodes in the graph, and white matter tracts the connections. The overall effect of an injury can then ...

Assortativity index (A. Index) of real-world network graphs has been traditionally computed based on the degree centrality metric and the networks were classified as assortative, dissortative or neutral if the A. Index values are respectively greater than 0, less than 0 or closer to 0. In this paper, we evaluate the A. Index of real-world network graphs based on some of the commonly used centra...

entrality egree loseness etweenness itality measures Centrality measures are based upon the structural position an actor has within the network. Induced centrality, sometimes called vitality measures, take graph invariants as an overall measure and derive vertex level measures by deleting individual nodes or edges and examining the overall change. By taking the sum of standard centrality measur...

Betweenness centrality ranks the importance of nodes by their participation in all shortest paths of the network. Therefore computing exact betweenness values is impractical in large networks. For static networks, approximation based on randomly sampled paths has been shown to be significantly faster in practice. However, for dynamic networks, no approximation algorithm for betweenness centrali...

In computer networks and social networks, the betweenness centrality of a node measures the amount of information passing through the node when all pairs are conducting shortest path exchanges. In this paper, we introduce a strategic network formation game in which nodes build connections subject to a budget constraint in order to maximize their betweenness in the network. To reflect real world...

Ernesto Estrada Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK The discriminant power of centrality indices for the degree, eigenvector, closeness, betweenness and subgraph centrality is analyzed. It is defined by the number of graphs for which the standard deviation of the centrality of its nodes is zero. On the basis of empirical analysis it is conclud...

Networks of social relations can be represented by graphs and socioor adjacency-matrices and their structure can be analyzed using different concepts, one of them called centrality. We will provide a new formalization of a “node-centrality” which leads to some properties a measure of centrality has to satisfy. These properties allow to test given measures, for example measures based on degree, ...