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A review on statistical physics for the sparsity of complex networks

Most practically existing complex networks are sparsely connected,namely,the average degrees of them are much smaller than their total numbers of nodes:k N.Up till now,the research on the origin of this property,its effects on functions of networks and dynamic processes on networks,and its possible applications have been still far less than adequate.Actually,sparsity is closely related with other topological properties.In recent years,much progress has been made on sparseness of complex networks from both theoretic and experimental aspects.However,principle conclusion is still anticipated.From the view point of statistical physics,it is believed that the sparsity of networks should be accounted as an emergent property of interactions between individuals in complex systems,instead of a priori prerequisite for existing models.In the present paper,we attempt to review previous investigations with statistical physics on the sparseness of complex networks.