a novel algorithm for the fast detection of hubs in chemical networks is presented. thealgorithm identifies a set of nodes in the network as most significant, aimed to be the mosteffective points of distribution for fast, widespread coverage throughout the system. we showthat our hubs have in general greater closeness centrality and betweenness centrality thanvertices with maximal degree, while...

Betweenness centrality is a quantity that is frequently used to measure how ‘central’ a vertex v is. It is defined as the sum, over pairs of vertices other than v, of the proportions of shortest paths that pass through v. In this paper, we study the distribution of the betweenness centrality in random trees and related, subcritical graph families. Specifically, we prove that the betweenness cen...

Within graph theory and network analysis, centrality of a vertex measures the relative importance of a vertex within a graph. The centrality plays key role in network analysis and has been widely studied using different methods. Inspired by the idea of vertex centrality, a novel centrality guided clustering (CGC) is proposed in this paper. Different from traditional clustering methods which usu...

Betweenness centrality of a vertex in a graph measures the fraction of shortest paths going through the vertex. This is a basic notion for determining the importance of a vertex in a network. The kbetweenness centrality of a vertex is defined similarly, but only considers shortest paths of length at most k. The sequence of k-betweenness centralities for all possible values of k forms the betwee...

The centrality of vertices has been a key issue in network analysis. For unweighted networks where edges are just present or absent and have no weight attached, many centrality measures have been presented, such as degree, betweenness, closeness, eigenvector and subgraph centrality. There has been a growing need to design centrality measures for weighted networks, because weighted networks wher...

Estimating the relative importance of vertices and edges is a fundamental issue in the analysis of complex networks, and has found vast applications in various aspects, such as social networks, power grids, and biological networks. Most previous work focuses on metrics of vertex importance and methods for identifying powerful vertices, while related work for edges is much lesser, especially for...

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.

Centrality analysis determines the importance of vertices in a network based on their connectivity within the network structure. It is a widely used technique to analyse network-structured data. A particularly important task is the comparison of different centrality measures within one network. We present three methods for the exploration and comparison of centrality measures within a network: ...

The centrality of a vertex v in a network intuitively captures how important v is for communication in the network. The task of improving the centrality of a vertex has many applications, as a higher centrality often implies a larger impact on the network or less transportation or administration cost. In this work we study the parameterized complexity of the NP-complete problems Closeness Impro...