We present an incremental algorithm that updates the betweenness centrality (BC) score of all vertices in a graph G when a new edge is added to G, or the weight of an existing edge is reduced. Our incremental algorithm runs in O(ν∗ · n) time, where ν∗ is bounded by m∗, the number of edges that lie on a shortest path in G. We achieve the same bound for the more general incremental vertex update ...

In this paper, we present some preliminary results indicating that Complex Network properties may be useful to improve performance of Active Learning algorithms. In fact, centrality measures derived from networks generated from the data allow ranking the instances to find out the best ones to be presented to a human expert for manual classification. We discuss how to rank the instances based on...

Network-analysis literature is rich in node-centrality measures that quantify the centrality of a node as a function of the (shortest) paths of the network that go through it. Existing work focuses on defining instances of such measures and designing algorithms for the specific combinatorial problems that arise for each instance. In this work, we propose a unifying definition of centrality that...

In real world complex networks, the importance of a node depends on two important parameters: 1. characteristics of the node, and 2. the context of the given application. The current literature contains several centrality measures that have been defined to measure the importance of a node based on the given application requirements. These centrality measures assign a centrality value to each no...

We present fully dynamic algorithms for maintaining betweenness centrality (BC) of vertices in a directed graph G = (V,E) with positive edge weights. BC is a widely used parameter in the analysis of large complex networks. We achieve an amortized O(ν∗ · log n) time per update with our basic algorithm, and O(ν∗ · log n) time with a more complex algorithm, where n = |V |, and ν∗ bounds the number...

Systems that capture and store data provenance, the record of how an object has arrived at its current state, accumulate historical metadata over time, forming a large graph. Local clustering in these graphs, in which we start with a seed vertex and grow a cluster around it, is of paramount importance because it supports critical provenance applications such as identifying semantically meaningf...

let g_1 and g_2 be simple connected graphs with disjoint vertex sets v(g_1) and v(g_2), respectively. for given vertices a_1in v(g_1) and a_2in v(g_2), a splice of g_1 and g_2 by vertices a_1 and a_2 is defined by identifying the vertices a_1 and a_2 in the :union: of g_1 and g_2. in this paper, we present exact formulas for computing some vertex-degree-based graph invariants of splice of graphs.

Centrality is an important notion in complex networks; it could be used to characterize how influential a node or an edge is in the network. It plays an important role in several other network analysis tools including community detection. Even though there are a small number of axiomatic frameworks associated with this notion, the existing formalizations are not generic in nature. In this paper...