Abstract: One of the common approaches for the community detection in complex networks is the Girvan-Newman algorithm [5] which is based on repeated deletion of edges having the maximum edge betweenness centrality. Although widely used, it may result in different dendrograms of hierarchies of communities if there are several edges eligible for removal (see [6]) thus leaving an ambiguous formati...

We present a fully dynamic algorithm for maintaining approximate maximum weight matching in general weighted graphs. The algorithm maintains a matchingM whose weight is at least 1 8M ∗ where M∗ is the weight of the maximum weight matching. The algorithm achieves an expected amortized O(logn log C) time per edge insertion or deletion, where C is the ratio of the weights of the highest weight edg...

Mader and Jackson independently proved that every 2-connected simple graph G with minimum degree at least four has a removable cycle, that is, a cycle C such that G\E(C) is 2-connected. This paper considers the problem of determining when every edge of a 2-connected graph G, simple or not, can be guaranteed to lie in some removable cycle. The main result establishes that if every deletion of tw...

A connected graph is said to be super edge-connected if every minimum edge-cut isolates a vertex. The restricted edge-connectivity λ′ of a connected graph is the minimum number of edges whose deletion results in a disconnected graph such that each component has at least two vertices. It has been shown by A. H. Esfahanian and S. L. Hakimi [On computing a conditional edge-connectivity of a graph....

We consider the problem of maintaining a dynamic planar graph subject to edge insertions and edge deletions that preserve planarity but that can change the embedding. We describe algorithms and data structures for maintaining information about 2and 3-vertex-connectivity, and 3and 4-edge-connectivity in a planar graph in O(n1/2) amortized time per insertion, deletion, or connectivity query. All ...

In an edge modification problem one has to change the edge set of a given graph as little as possible so as to satisfy a certain property. We prove the NP-hardness of a variety of edge modification problems with respect to some well-studied classes of graphs. These include perfect, chordal, chain, comparability, split and asteroidal triple free. We show that some of these problems become polyno...

The common causes of 18p deletion syndrome are spontaneous errors in the chromosomal structure in the early stages of human embryonic development. In this study, a 29-year-old girl was introduced with the features of deletion of chromosome 18. In addition, GTG banding karyotype revealed that this case had a deletion involving the short arm of chromosome 18. In comparison with the usual phenotyp...

First posed in 1942 by Kelly and Ulam, the Graph Reconstruction Conjecture is one of the major open problem in graph theory. While the Graph Reconstruction Conjecture remains open, it has spawned a number of related questions. In the classical vertex graph reconstruction number problem a vertex is deleted in every possible way from a graph G, and then it can be asked how many (both minimum and ...

The growth and evolution of networks has elicited considerable interest from the scientific community and a number of mechanistic models have been proposed to explain their observed degree distributions. Various microscopic processes have been incorporated in these models, among them, node and edge addition, vertex fitness and the deletion of nodes and edges. The existing models, however, focus...