title: Reconstructing direct and indirect interactions in networked public goods game.
abstract: Network reconstruction is a fundamental problem for understanding many complex systems with unknown interaction structures. In many complex systems, there are indirect interactions between two individuals without immediate connection but with common neighbors. Despite recent advances in network reconstruction, we continue to lack an approach for reconstructing complex networks with indirect interactions. Here we introduce a two-step strategy to resolve the reconstruction problem, where in the first step, we recover both direct and indirect interactions by employing the Lasso to solve a sparse signal reconstruction problem, and in the second step, we use matrix transformation and optimization to distinguish between direct and indirect interactions. The network structure corresponding to direct interactions can be fully uncovered. We exploit the public goods game occurring on complex networks as a paradigm for characterizing indirect interactions and test our reconstruction approach. We find that high reconstruction accuracy can be achieved for both homogeneous and heterogeneous networks, and a number of empirical networks in spite of insufficient data measurement contaminated by noise. Although a general framework for reconstructing complex networks with arbitrary types of indirect interactions is yet lacking, our approach opens new routes to separate direct and indirect interactions in a representative complex system.
authors.affiliation: School of Systems Science, Beijing Normal University, Beijing, 100875, P. R. China.
authors.forename: Xiao
authors.initials: X
authors.lastname: Han
authors.affiliation: School of Systems Science, Beijing Normal University, Beijing, 100875, P. R. China.
authors.forename: Zhesi
authors.initials: Z
authors.lastname: Shen
authors.affiliation: School of Systems Science, Beijing Normal University, Beijing, 100875, P. R. China.|Business School, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China.
authors.forename: Wen-Xu
authors.initials: WX
authors.lastname: Wang
authors.affiliation: School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA.
authors.forename: Ying-Cheng
authors.initials: YC
authors.lastname: Lai
authors.affiliation: Institute for Complex Systems and Mathematical Biology, Kings College, University of Aberdeen, Aberdeen AB24 3UE, UK.
authors.forename: Celso
authors.initials: C
authors.lastname: Grebogi