Graph burning is a model for spread of information in network. In recent times social networks play major role the thought process people and influences movements, election politics. The number an ideal to calculate speed at which passed throughout burns graph minimum steps. this paper, hybrid algorithm proposed compute network based on selection activators. uses spanning tree, weighted central...

Betweenness centrality is a distance-based invariant of graphs. In this paper, we use lexicographic product to compute betweenness centrality of some important classes of graphs. Finally, we pose some open problems related to this topic.

The most popular method of drawing directed graphs is to place vertices on a set of horizontal or concentric levels, known as level drawings. Level drawings are well studied in Graph Drawing due to their strong application for the visualization of hierarchy in graphs. There are two drawing conventions: horizontal drawings use a set of parallel lines and radial drawings use a set of concentric c...

Given an n-vertex m-edge graph G of clique-width at most k, and a corresponding k-expression, we present algorithms for computing some well-known centrality indices (eccentricity closeness) that run in $${\mathcal {O}}(2^{{\mathcal {O}}(k)}(n+m)^{1+\epsilon })$$ time any $$\epsilon > 0$$ . Doing so, can solve various distance problems within the same amount time, including: diameter, center, Wi...

We consider the all pairs all shortest paths (APASP) problem, which maintains all of the multiple shortest paths for every vertex pair in a directed graph G = (V,E) with a positive real weight on each edge. We present a fully dynamic algorithm for this problem in which an update supports either weight increases or weight decreases on a subset of edges incident to a vertex. Our algorithm runs in...

In this paper, we thoroughly investigate correlations of eigenvector centrality to five centrality measures, including degree centrality, betweenness centrality, clustering coefficient centrality, closeness centrality, and farness centrality, of various types of network (random network, smallworld network, and real-world network). For each network, we compute those six centrality measures, from...

We present a social tag recommendation model for collaborative bookmarking systems. This model receives as input a bookmark of a web page or scientific publication, and automatically suggests a set of social tags useful for annotating the bookmarked document. Analysing and processing the bookmark textual contents document title, URL, abstract and descriptions we extract a set of keywords, formi...

Topological centrality is a significant measure for characterising the relative importance of a node in a complex network. For directed networks that model dynamic processes, however, it is of more practical importance to quantify a vertex's ability to dominate (control or observe) the state of other vertices. In this paper, based on the determination of controllable and observable subspaces un...

Distance-based indices, including closeness centrality, average path length, eccentricity and average eccentricity, are important tools for network analysis. In these indices, the distance between two vertices is measured by the size of shortest paths between them. However, this measure has shortcomings. A well-studied shortcoming is that extending it to disconnected graphs (and also directed g...

Networks of social relations can be represented by graphs and socioor adjacency-matrices and their structure can be analyzed using different concepts, one of them called centrality. We will provide a new formalization of a “node-centrality” which leads to some properties a measure of centrality has to satisfy. These properties allow to test given measures, for example measures based on degree, ...