WICER: a weighted inter-cluster edge ranking for clustered graphs

Several algorithms based on link analysis have been developed to measure the importance of nodes on a graph such as pages on the World Wide Web. PageRank and HITS are the most popular ranking algorithms to rank the nodes of any directed graph. But, both these algorithms assign equal importance to all the edges and nodes, ignoring the semantically rich information from nodes and edges. Therefore, in the case of a graph containing natural clusters, these algorithms do not differentiate between inter-cluster edges and intra-cluster edges. Based on this parameter, we propose a weighted inter-cluster edge ranking for clustered graphs that weighs edges (based on whether it is an inter-cluster or an intra-cluster edge) and nodes (based on the number of clusters it connects). We introduce a parameter ´α´ which can be adjusted depending on the bias desired in a clustered graph. Our experiments were two fold. We implemented our algorithm to a relationship set representing legal entities and documents and the results indicate the significance of the weighted edge approach. We also generated biased and random walks to quantitatively study the performance.