We give the first O(t log t) time algorithm for processing a given sequence of t edge updates and 3-vertex/edge connectivity queries in an undirected unweighted graph. Our approach builds upon a method by Eppstein [Epp94] that reduces graphs to smaller equivalents on a set of key vertices. It also leads to algorithms for offline 2-vertex/edge connectivity whose performances match those from Kac...

In this paper we present a study about spanning edge betweenness, an edge-based metric for complex network analysis that is defined as the probability of an edge being part of a minimum spanning tree. This probability reflects how redundant an edge is in what concerns the connectivity of a given network and, hence, its value gives information about the network topology. We apply this metric to ...

In this paper, a new method for edge detection in presence of impulsive noise based into the use of Support Vector Machines (SVM) is presented. This method shows how the SVM can detect edge in an efficient way. The noisy images are processed in two ways, first reducing the noise by using the SVM regression and then performing the classification using the SVM classification. The results presente...

Restricted edge connectivity is a more refined network reliability index than edge connectivity. A restricted edge cut F of a connected graph G is an edge cut such that G−F has no isolated vertex. The restricted edge connectivity λ′ is theminimumcardinality over all restricted edge cuts.WecallG λ′-optimal if λ′ = ξ , where ξ is theminimum edgedegree inG. Moreover, a λ′-optimal graphG is called ...

Let G = (V, E) be a connected graph. Let G = (V, E) be a connected graph. An edge set F ⊂ E is said to be a k-restricted edge cut, if G− F is disconnected and every component of G− F has at least k vertices. The k-restricted edge connectivity of G, denoted by λk(G), is the cardinality of a minimum k-restricted edge cut of G. A graph G is λk-connected, if G contains a k-restricted edge cut. A λk...