Traveling salesman problems with PageRank Distance on complex networks reveal community structure

• Community detection problems are transformed to traveling salesman problems (TSPs).
• A distance measure based on PageRank is designed in TSPs.
• A threshold-based method is designed to transform the tours in TSPs to communities.
• A TSP-based community detection method, termed as TSP-CDA, is proposed.
• Networks with up to 10,000 nodes and varying structures are used in experiments.

In this paper, we propose a new algorithm for community detection problems (CDPs) based on traveling salesman problems (TSPs), labeled as TSP-CDA. Since TSPs need to find a tour with minimum cost, cities close to each other are usually clustered in the tour. This inspired us to model CDPs as TSPs by taking each vertex as a city. Then, in the final tour, the vertices in the same community tend to cluster together, and the community structure can be obtained by cutting the tour into a couple of paths. There are two challenges. The first is to define a suitable distance between each pair of vertices which can reflect the probability that they belong to the same community. The second is to design a suitable strategy to cut the final tour into paths which can form communities. In TSP-CDA, we deal with these two challenges by defining a PageRank Distance and an automatic threshold-based cutting strategy. The PageRank Distance is designed with the intrinsic properties of CDPs in mind, and can be calculated efficiently. In the experiments, benchmark networks with 1000–10,000 nodes and varying structures are used to test the performance of TSP-CDA. A comparison is also made between TSP-CDA and two well-established community detection algorithms. The results show that TSP-CDA can find accurate community structure efficiently and outperforms the two existing algorithms.