Laplacian Spectral Properties of Complex Networks
【摘要】:We consider spectral analysis of complex networks.It is well known that the eigenvalue spectrum of complex networks provides information about their structural properties.Therefore,we present spectral properties of some different real-world networks such as regular networks,random networks,small-world networks,scale-free networks,and so on.We find that in random networks,the smallest nonzero eigenvalue grows approximately linearly with respect to the probability p.As a result of this,some estimates for the smallest nonzero eigenvalues of random networks can be obtained.More interestingly,it is shown a strong correlation between the eigenvalue spectrum and degree sequence in the networks,especially in scale-free networks.Making use of this correlation,we develop a local algorithm to determine the eigenvalue λi+1 from λi.