The Study Of Percolation Phase Transition Modle And Homology Of Complex Network

In our real life,the network is everywhere,and we are all in a complex network system.The research of complex networks is a hot topic,and many experts and scholars have devoted themselves to it.The study of complex networks can help people better understand the network,manage network,do network planning and optimization.Many research results are to be directly applied to the real life,but also greatly enriched the theory of complex network.Percolation theory derived from statistical physics,is a powerful tool for studying the structure of disordered and stochastic systems.The network percolation transition theory has great role in the research of functional stability of the networks.This paper mainly studies the complex network percolation model and network homology.Firstly,we use percolation theory in the network,and establish complex network percolation transition model.The critical value of probability of the disappearance and emergence of the giant component in the random network and scale-free network is analyzed.At the same time,we also construct complex networks using simplicial complexes in algebraic topology,and study the homology in different network models.Some topological homology parameters are derived by topological homology group and Betti number.And the network phase transition of homology parameter under different attack strategies is also studied.The relation between homology parameter and connectivity of the network is analyzed.Finally,the robustness of complex networks are discussed combining with the existing results we have gained.The critical values of percolation transition probabilities for different networks are obtained by using the generating function.Through MATLAB numerical simulation,we use random attack strategy to attack network node in the random networks and scale-free networks.Through the changes of network giant component,we obtain random networks and scale-free networks' percolation phase transition phenomenon and the law of phase transition,the experimental results can match our theoretical results well.We construct complex networks using simplicial complexes in algebraic topology,and introduce the topology homology group and Betti number of networks,and analyze the persistent homology of weighted networks.We obtained the existence and vanishing intervals of network homology groups,and propose some topological homology parameters.Combining with the percolation transition model of network,we do the numerical simulation in random network,scale-free network and real network respectively.The phase transition phenomenon of homology parameters in different network models is obtained by data visualization.Numerical simulations of random networks,scale-free networks and real networks are performed using MATLAB.It is found that homology parameters are closely related to network connectivity.We introduce the network robustness index and vulnerability index,We combine the percolation theory and network topology homology parameter to analyze the robustness of the network.We make random attacks and deliberate attacks on nodes in random networks,scale-free networks and real networks,through MATLAB numerical simulation,the relationship between the network robustness index,homology parameters and attack probability under different attack strategies is obtained.Combining homogeneous index,we find that the more homogeneous the network is,the better the robustness to deliberate attack,the more unhomogeneous the network is,the better robustness to response random failures.In the end,our experimental results can match well with the theory,and the ideal results are obtained.