Let G(V,E1) and G (V,E2) be two networks on the same vertex set V and consider the union of edges G(V,E1 ∪ E2). This paper studies the stability of the Degree, Betweenness and Eigenvector Centrality of the resultant network, G(V,E1 ∪ E2). Specifically assume v max and v max are the highest centrality vertices of G(V,E1) and G(V,E1 ∪ E2) respectively, we want to find Pr(v max = v max). ar X iv :...

Betweenness centrality, measuring how many shortest paths pass through a vertex, is one of the most important network analysis concepts for assessing the (relative) importance of a vertex. The famous state-of-art algorithm of Brandes [2001] computes the betweenness centrality of all vertices in O(mn) worst-case time on an n-vertex and m-edge graph. In practical follow-up work, significant empir...

This paper presents a novel method for layout of undirected graphs, where nodes (vertices) are constrained to lie on a set of nested, simple, closed curves. Such a layout is useful to simultaneously display the structural centrality and vertex distance information for graphs in many domains, including social networks. Closed curves are a more general constraint than the previously proposed circ...

In a connected graph, spanning tree centralities of a vertex and an edge measure how crucial they are for the graph to be connected. In this paper, we propose efficient algorithms for estimating spanning tree centralities with theoretical guarantees on their accuracy. We experimentally demonstrate that our methods are orders of magnitude faster than previous methods. Then, we propose a novel ce...

Structure of real networked systems, such as social relationship, can be modeled as temporal networks in which each edge appears only at the prescribed time. Understanding the structure of temporal networks requires quantifying the importance of a temporal vertex, which is a pair of vertex index and time. In this paper, we define two centrality measures of a temporal vertex based on the fastest...

Betweenness centrality of a vertex (edge) in a graph is a measure for the relative participation of the vertex (edge) in the shortest paths in the graph. Betweenness centrality is widely used in various areas such as biology, transportation, and social networks. In this paper, we study the update problem of betweenness centrality in fully dynamic graphs. The proposed update algorithm substantia...

Planarisation of graphs is a well studied research problem in Graph Theory and has important applications in Graph Drawing to draw non-planar graphs with as few crossings as possible. However, the problem of finding the maximum vertex (or edge) induced planar subgraph NP-hard. Centrality index is one of the important concepts in Network Analysis for analysing the importance of actors in the soc...

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...

The study of complex networks has recently attracted increasing interest because of the large variety of systems that can be modeled using graphs. A fundamental operation in the analysis of complex networks is that of measuring the centrality of a vertex. In this paper, we propose to measure vertex centrality using a continuous-time quantum walk. More specifically, we relate the importance of a...