Topology Description Based On Optimal Feature Space Of Complex Network's Statistical Properties

Topology of complex network determines its function and dynamic.Therefore,both the expression of network's topology and the topological analysis based on it are important research topics in complex network analysis.Besides fundamental representation coming from graph theory,many kinds of statistical properties are also used to describe network's topology.Because single statistical property could only partially reflect the topological structure of network,a novel method is proposed in this paper in order to seek for an optimal set of properties distinguishing different topologies.The proposed method is based on the concept of multi-dimensional feature space in which networks are mapped into feature vectors.The strategy is to find the feature space constructed out of the best combination of statistical properties of network in accordance with class separability and other criteria about sample sets.Groups of sample sets are generated respectively by typical evolving models.SVM classifier is utilized to confirm that the sample sets could be considered as separable classes with different pure topologies.The initial 20 statistical properties of network are selected according to computability and the correlation with topology.Then the process of dimension reduction is conducted by branchand-bound algorithm.The criterion function reflects the compactness of classes,the feature independence and the correlation between features and network scale.The 13 optimal statistical properties are found finally.Typical evolving model networks,sampling subnets and some real networks are used in the experiments to examine the optimal property set through topological similarity analysis and evaluation of sampling method.The results show that mapping from complex network's topology to the 13-dimensional feature space is reasonable and the similarity measurement,distance of two feature vectors,in the feature space is effective.The proposed method provides a new idea to the research of topology of complex network and it is significant for network structure analysis and its application.