| As interdiscipline subject of mathematics,statistics,physics,computer science,life sciences and other disciplines,network science is under the circumstance of fast development.Many empirical studies have shown that chemistry,ecology,meteorology,economics and other disciplines in the field of systems,while complicated,but behind it are some common features,like scale-free,small-world,emergent,self-organization and self-similarity.Aims at searching for the mechanism behind these common features,the network science can be used to forecast and even control complex systems.The paper is devoted to research on dynamics of complex network evolution and find simple mechanism behind the complicated network.Based on the analysis of real network data,the paper use a range of mathematical tools e.g.matrix,game and geometry to,and other widely used for the model the network evolution,predict the network linkage,and explain the nature of network statistics properties.Main contents and contributions of this paper including:1.The mechanisms of links formation and link prediction.Combination of network information at different scales,in particular clustering information,a probability model is proposed via statistical inference.Based on the model,a link prediction algorithm is proposed through nonnegative matrix factorization and clustering information.A bi-scale link prediction algorithm is proposed with consideration of both micro-scale and mesoscale clustering information.Further,a network link prediction metrics is proposed based on neighbors’ communities.Theoretical analysis and experiment contrast demonstrates the prediction results of the three methods.2.The geometric presentation of network evolution.Many real network data showed that there is geometry behind the network.Therefore,the paper study the network evolution with geometry.Two different Mechanisms are analyzed in real networks,according to witch a bi-layer network model is proposed.Networks generated by the model have similar degree distribution and clustering coefficient with real data.A growth concentric circle model is proposed to model the scientific network,experiments show that the model can reproduce many properties in real networks.Meanwhile,the critical point of degree distribution is analyzed in the model.3.Modelling and analyzing the game mechanisms in network evolution.Complex network has self-organizability,in which nodes in many network have full autonomy.Under the node fully rational hypothesis,the network evolution process is analyzed through game theory.Many network properties,like scale-free,assortativity and small world,is reproduced by the majority game,coordination game and other forms of game.In addition,sociological reasonable explanation is presented for those properities.Further the relationships between the node tolerance of noncooperation and the rate of cooperation is analyzed in the framework of public goods Game. |
