Community Detection,Link Prediction And Applications In Complex Networks

A dynamical clustering model of discrete-time networks is proposed in this paper,based on the classic Kuramoto model.There are two main improvements in the new model.First,the differential equation in the original Kuramoto model is replaced by a difference equation.The computation of the difference equation is much less time-consuming,compared with that of the differential equation.Second,the coupling strength in the original Kuramoto model is replaced by a new coupling strength,containing a positive coupling strength and a negative coupling strength.Thus a dynamical clustering phenomenon is observed in the discrete-time networks with community structure.There is only one positive coupling strength in the original Kuramoto model,so all connected nodes appeal to each other,when the original model is used to study the dynamical behaviors of nodes in complex networks.And all nodes in a network will converge to a state of global synchronization,if the coupling strength exceeds a specific value.But when a negative coupling strength is added to the model,there exist two kinds of interactions among nodes: an attractive interaction and a repulsive interaction.The connected nodes appeal to each other due to the attractive interaction;while the unconnected nodes repulse each other due to the repulsive interaction.The phases of connected nodes evolve nearer to each other;while the phases of unconnected nodes evolve further from each other,because of the two reciprocal interactions.Therefore,the dynamical clustering phenomenon appears in the dynamical clustering model.As iteration starts,the phases of nodes evolve into clusters after a transient state of oscillation.The nodes that belong to one community have phases in one cluster.After an introduction of clustering phenomenon,this paper describes the slowing decaying state of frequencies in the evolution of phases and mathematically analyzes the relationship between the frequency and the slowest decaying eigenvector of a transfer matrix corresponding to the dynamical clustering model.The analytical and experimental results both show that the slowest decaying eigenvector corresponds to the frequencies of all nodes in the network.Previous works and experimental results both prove that the frequency in the evolution of phase contains community structure information as the phase does.The main content of this paper is as follows.Firstly,the dynamical clustering model of discrete-time networks can be used directly in finding community structure in complex networks.Communities can be detected by phases of nodes and frequencies in the evolution of the phases.Based on the dynamical clustering model of discrete-time networks,an algorithm for community detection is proposed in this paper.Its detailed process is provided.And the algorithm is proved to be highly efficient and accurate over a recently-proposed,modularity-based algorithm through experiments.Secondly,the dynamical clustering of nodes can be used in breast mass detection.In this paper,a mass detection algorithm is proposed based on the dynamical clustering model of discrete-time networks.An image pretreatment and feature extraction are done before the mass detection.The image is divided into irregular regions by the watershed transform and features of all regions are calculated.And a network denoted by a graph is constructed from the features and regions.Then the phases of nodes in the network are clustered though iterating the dynamical clustering model.The clusters of the phases of nodes correspond to clusters of the regions in the image,in which way a segmentation result is obtained at last.The experiments show that the proposed mass detection algorithm is effective,compared with two classic algorithms named K-means and FCM.Thirdly,it is known that community structure information can be used in link prediction of complex networks from previous works.In this paper,similarity indexes between nodes are defined by the phase and frequency in the dynamical clustering model.Experiments show the effectiveness of both real community structure information and community structure information extracted by an algorithm for community detection,used in link prediction of real-world and artificial networks.The performance of the phase-based and frequency-based indexes are shown in experiments and proved to be effect too.At last,due to the idea of using community information in link prediction of complex networks,different kinds of information are fused with community information to do link prediction.Based on the function of density of modularity,an improved algorithm is applied to extract community information.The extracted community information defines a similarity index and further fuses with information about degrees of nodes and transition probability.Based on the obtained fusion information,an algorithm is proposed for link prediction.Experiments are done on large-scale,real-world networks.Community information fuses with different kinds of information.And the indexes based on the fusion information are proved to be effective.Compared with the existing indexes and other link prediction methods using community information,the proposed algorithm shows its high efficiency and accuracy.