Reconstruction of networks from one-step data by matching positions

Abstract

h i g h l i g h t s• A method for reconstructing the topology of networks with only one step data. • This algorithm utilizes the natural sparsity and degree distribution of real world networks.• The problem of matching position is defined and a simple algorithm is developed.• The matching position can be used in network reconstruction and other problems.• The proposed method is verified in networks with ten thousands of vertices. a b s t r a c tIt is a challenge in estimating the topology of a network from short time series data. In this paper, matching positions is developed to reconstruct the topology of a network from only one-step data. We consider a general network model of coupled agents, in which the phase transformation of each node is determined by its neighbors. From the phase transformation information from one step to the next, the connections of the tail vertices are reconstructed firstly by the matching positions. Removing the already reconstructed vertices, and repeatedly reconstructing the connections of tail vertices, the topology of the entire network is reconstructed. For sparse scale-free networks with more than ten thousands nodes, we almost obtain the actual topology using only the one-step data in simulations.