Locating dense and isolated sub-graphs through constructing auxiliary weighted graph

Abstract

Methods and apparatus for locating a dense and isolated sub-graph from a weighted graph having multiple nodes and multiple weighted edges are described. Each node in the weighted graph represents an object. Each weighted edge in the weighted graph connects two nodes and represents the relationship between the two objects represented by the two corresponding nodes. To located the sub-graph, first, an auxiliary weighted graph is constructed using the weighted graph and three coefficients: α, β, and γ, where α, β, and γ are greater than 0, α influences the number of nodes inside the sub-graph, β influences the sum of the weights associated with the edges connecting a node inside the sub-graph and a node outside the sub-graph, and γ influences the sum of the weights associated with the edges connecting two nodes both inside the sub-graph, and by adding a source node s and a sink node t. Next, the auxiliary weighted graph is partitioned into two parts using the s-t minimum cut algorithm. The sub-graph is the part associated with the sink node t in its original form, with the original undirected edges and unmodified edge weights and excluding the sink node t and all the new edges added during the construction of the auxiliary weighted graph.