An Experimental Study on Centrality Measures Using Clustering

Abstract

Graphs can be found in almost every part of modern life: social networks, road networks, biology, and so on. Finding the most important node is a vital issue. Up to this date, numerous centrality measures were proposed to address this problem; however, each has its drawbacks, for example, not scaling well on large graphs. In this paper, we investigate the ranking efficiency and the execution time of a method that uses graph clustering to reduce the time that is needed to define the vital nodes. With graph clustering, the neighboring nodes representing communities are selected into groups. These groups are then used to create subgraphs from the original graph, which are smaller and easier to measure. To classify the efficiency, we investigate different aspects of accuracy. First, we compare the top 10 nodes that resulted from the original closeness and betweenness methods with the nodes that resulted from the use of this method. Then, we examine what percentage of the first n nodes are equal between the original and the clustered ranking. Centrality measures also assign a value to each node, so lastly we investigate the sum of the centrality values of the top n nodes. We also evaluate the runtime of the investigated method, and the original measures in plain implementation, with the use of a graph database. Based on our experiments, our method greatly reduces the time consumption of the investigated centrality measures, especially in the case of the Louvain algorithm. The first experiment regarding the accuracy yielded that the examination of the top 10 nodes is not good enough to properly evaluate the precision. The second experiment showed that the investigated algorithm in par with the Paris algorithm has around 45–60% accuracy in the case of betweenness centrality. On the other hand, the last experiment resulted that the investigated method has great accuracy in the case of closeness centrality especially in the case of Louvain clustering algorithm.

Keywords

• centrality
• betweenness
• closeness
• graph clustering
• Markov algorithm
• Louvain algorithm