Stress is a centrality measure determined by the shortest paths passing through given vertex. Noting that adjacency matrix playing an important role in finding distance and number of between pair vertices, interesting expression also algorithm are presented to find stress using matrix. The results suitably adopted obtain betweenness measure. Further extended cases Cartesian product G□H graphs, ...

It is common for people to access multiple social networks, for example, using phone, email, and social media. Together, the multi-layer social interactions form a “integrated social network.” How can we extend well developed knowledge about single-layer networks, including vertex centrality and community structure, to such heterogeneous structures? In this paper, we approach these challenges b...

We study a problem of data packet transport in scale-free networks whose degree distribution follows a power law with the exponent gamma. Load, or "betweenness centrality," of a vertex is the accumulated total number of data packets passing through that vertex when every pair of vertices sends and receives a data packet along the shortest path connecting the pair. It is found that the load dist...

We analyze directed, unweighted graphs obtained from xi ∈ R by connecting vertex i to j iff |xi − xj | < ε(xi). Examples of such graphs include k-nearest neighbor graphs, where ε(xi) varies from point to point, and, arguably, many real-world graphs such as copurchasing graphs. We ask whether we can recover the underlying Euclidean metric ε(xi) and the associated density p(xi) given only the dir...

For almost a decade, it has been found that many physical, biological, and social systems are properly described by complex networks in which a vertex represents each individual element and an edge denotes the interaction between a pair of vertices. These networks have been revealed that they share some non-trivial topological properties such as the scale-free degree distribution, P(k) ~k -γ . ...

Centrality is a family of metrics for characterizing the importance vertex in graph. Although large number centrality have been proposed, majority them ignores uncertainty graph data. In this paper, we formulate closeness on uncertain graphs and define batch evaluation problem that computes subset vertices an We develop three algorithms, MS-BCC , MG-BCC MGMS-BCC based sampling to approximate sp...

Measuring the relative importance of each vertex in a network is one of the most fundamental building blocks in network analysis. Among several importance measures, betweenness centrality, in particular, plays key roles in many real applications. Considerable effort has been made for developing algorithms for static settings. However, real networks today are highly dynamic and are evolving rapi...

Many networks are dynamic in that their topology changes rapidly--on the same time scale as the communications of interest between network nodes. Examples are the human contact networks involved in the transmission of disease, ad hoc radio networks between moving vehicles, and the transactions between principals in a market. While we have good models of static networks, so far these have been l...

Abstract This paper introduces the notions of chained and semi-chained graphs. The chain a graph, when existent, refines notion bipartivity conveys important structural information. Also center vertex $$v_c$$ v c is introduced. It vertex, whose sum p powers distances to...

Given two sets of entities – potentially the results of two queries on a knowledge-graph like YAGO or DBpedia– characterizing the relationship between these sets in the form of important people, events and organizations is an analytics task useful in many domains. In this paper, we present an intuitive and efficiently computable vertex centrality measure that captures the importance of a node w...