Despite persistent effort, there is no known technique for obtaining super-linear lower bounds for the computational complexity of the problems in P. Vassilevska Williams and Williams [38] introduce a fruitful approach to advance a better understanding of the computational complexity of the problems in P. In particular, they consider All Pairs Shortest Paths (APSP) and other fundamental problem...

This paper presents a centrality measurement and analysis of the social networks for tracking online community. The tracking of single community in social networks is commonly done using some of the centrality measures employed in social network community tracking. The ability that centrality measures have to determine the relative position of a node within a network has been used in previous r...

The author conducts an extensive correlation coefficient analysis of four prominent centrality measures for mobile ad hoc networks. The centrality measures considered are the degree-based degree centrality and eigenvector centrality, and the shortest path-based betweenness centrality and closeness centrality. The author evaluates the correlation coefficient between any two of the above four cen...

In the dynamic tree problem the goal is the maintenance of an arbitrary n-vertex forest, where the trees are subject to joining and splitting by, respectively, adding and removing edges. Depending on the application, information can be associated to nodes or edges (or both), and queries might require to combine values in path or (sub)trees. In this paper we present a novel data structure, calle...

Abstract Betweenness centrality quantifies the importance of a vertex for information flow in network. The standard betweenness applies to static single-layer networks, but many real world networks are both dynamic and made several layers. We propose definition temporal multiplexes. This accounts topological structure duration paths determination shortest paths. an algorithm compute new metric ...

We propose a generalized stochastic block model to explore the mesoscopic structures in signed networks by grouping vertices that exhibit similar positive and negative connection profiles into the same cluster. In this model, the group memberships are viewed as hidden or unobserved quantities, and the connection patterns between groups are explicitly characterized by two block matrices, one for...

Scale-free networks are a type of complex networks in which the degree distribution of the nodes is according to the power-law. Centrality of the nodes is a quantitative measure of the importance of the nodes according to the topological structure of the network. The commonly used centrality measures are the degree-based degree centrality and eigenvector centrality and the shortest path-based c...

Network structure analysis plays an important role in characterizing complex systems. Different from previous network centrality measures, this article proposes the topological centrality measure reflecting the topological positions of nodes and edges as well as influence between nodes and edges in general network. Experiments on different networks show distinguished features of the topological...

We study numerically the cascading failure problem by using artificially created scale-free networks and the real network structure of the power grid. The capacity for a vertex is assigned as a monotonically increasing function of the load (or the betweenness centrality). Through the use of a simple functional form with two free parameters, revealed is that it is indeed possible to make network...

This paper proposes a new node centrality measurement index (c-index) and its derivative indexes (iterative c-index and cg-index) to measure the collaboration competence of a node in a weighted network. We prove that c-index observe the power law distribution in the weighted scale-free network. A case study of a very large scientific collaboration network indicates that the indexes proposed in ...