Gravity algorithm for the community detection of large-scale network

Community detection refers to the task of finding groups of nodes in a network that share common properties. The identified groups are called communities, which have tight intra-connections and feeble inter-connections. For the large-scale networks, we need a stable algorithm to detect communities quickly and does not depend on previous knowledge about the possible communities and any special parameter tuning. Therefore, this paper introduces a novel algorithm for community detection that is inspired by the surface Gravity of astronomical objects. In this algorithm, each vertex of a network and its degree and size are metaphors for an astronomical object and its mass and radius, respectively. The algorithm defines the gravity force for each vertex of a network. So, as a dense astronomical object, a dense vertex has a high mass and a low radius and exerts a high gravity force on its neighbours. In this paper, we define a particular modularity gain function to evaluate the merging gain of two vertexes. The algorithm is very fast, and its computational complexity is from the order of O(nlog n) . Although there is a trade-off between the modularity and speed of algorithms, the results showed that the suggested algorithm is much faster than the current well-known algorithms. Furthermore, it is reliable, stable and free from parameter tuning as well as predefined knowledge about communities. In this paper, the proposed algorithm is extended to run faster than the original Gravity. The extended Gravity algorithm divides a large scale network into some smaller sub-networks. Then the communities of each part are detected in serial and parallel modes. By preserving the modularity of detected communities, the extended Gravity is extremely faster than the original Gravity algorithm.