Vertex betweenness centrality is essential in the analysis of social and information networks, and it quantify vertex importance in terms of its quantity of information along geodesic paths in network. Edge betweenness is similar to the vertex betweenness. Co-betweenness centrality is a natural developed notion to extend vertex betweenness centrality to sets of vertices, and pairwise co-between...

In a well-known paper [Social Networks 1 (1979) 215] Linton Freeman clarified the importance of the centrality concept in network analysis. There are a variety of centrality measures available, and they are mainly used as descriptive statistics in various network studies. For instance, actor centrality measured by vertex degree captures those aspects of centrality that have an impact on contact...

Closeness centrality is an important concept in social network analysis. In a graph representing a social network, closeness centrality measures how close a vertex is to all other vertices in the graph. In this paper, we combine existing methods on calculating exact values and approximate values of closeness centrality and present new algorithms to rank the top-k vertices with the highest close...

In this article we use Multiple Centrality Assessment (MCA) based on the idea of Sergio Porta [Por06]. We apply MCA for the urban streets of Tirana. MCA is based on primal, rather than dual, street graphs, it works within a metric, rather than topological, framework and it investigates a plurality of peer centrality indices. We show that, in the MCA primal approach, some centrality indices nice...

Betweenness is a centrality measure based on shortest paths, widely used in complex network analysis. It is computationally-expensive to exactly determine betweenness; currently the fastest-known algorithm by Brandes requires O(nm) time for unweighted graphs and O(nm + n log n) time for weighted graphs, where n is the number of vertices and m is the number of edges in the network. These are als...

The calculation of centrality measures is common practice in the study of networks, as they attempt to quantify the importance of individual vertices, edges, or other components. Different centralities attempt to measure importance in different ways. In this paper, we examine a conjecture posed by E. Estrada regarding the ability of several measures to distinguish the vertices of networks. Estr...

Betweenness centrality is a centrality measure that is widely used, with applications across several disciplines. It is a measure which quantifies the importance of a vertex based on its occurrence in shortest paths between all possible pairs of vertices in a graph. This is a global measure, and in order to find the betweenness centrality of a node, one is supposed to have complete information ...

Table 1 Correlation of vertex and edge frontier sizes with execution time for three randomly selected roots of different graph structures. The size of the vertex frontier correlates positively with execution time regardless of the root or structure of the graph.. Figure 1 Evolution of vertex frontiers (as a percentage of total vertices) for differ-Figure 4 Power consumption for various betweenn...

Analyzing massive graphs poses challenges due to the vast amount of data available. Extracting smaller relevant subgraphs allows for further visualization and analysis that would otherwise be too computationally intensive. Furthermore, many real data sets are constantly changing, and require algorithms to update as the graph evolves. This work addresses the topic of local community detection, o...