Scaling invariance in spectra of complex networks: A diffusion factorial moment approach

Abstract

A new method called diffusion factorial moment is used to obtain scaling features embedded in the spectra of complex networks. For an Erdos-Renyi network with connecting probability p(ER) < 1/N, the scaling parameter is delta = 0.51, while for p(ER) > or = 1/N the scaling parameter deviates from it significantly. For WS small-world networks, in the special region p(r) element of [0.05,0.2], typical scale invariance is found. For growing random networks, in the range of theta element of [0.33,049], we have delta = 0.6 +.- 0.1. And the value of delta oscillates around delta = 0.6 abruptly. In the range of delta element of [0.54,1], we have basically element of > 0.7. Scale invariance is one of the common features of the three kinds of networks, which can be employed as a global measurement of complex networks in a unified way.

Energy Spectral Behaviors of Communication Networks of Open-Source Communities

“…This paper extends the concept of quantum mapping of complex networks in references [ 18 – 20 ]. Here the quantum mapping not only refers to mapping nodes of a network to atoms in a large molecule and the edges to the chemical bonds between the atoms, but also refers to mapping an edge weight that reflects the connection intensity of a pair of nodes to the hopping energy required for an electron to jump between the atoms, and the node weight that reflects node attributes to the energy of the electron on the atom site to which it belongs, consequently a complex network is mapped to a large molecule.…”

“…Yang et al proposed a mapping from complex networks to quantum systems [ 18 – 20 ]. Suppose the adjacent matrix of a complex network with N identical nodes is A , whose elements A ij = 1 or 0 if the nodes i and j are connected or disconnected, respectively.…”

“…In this paper we first construct the complex network models of 12 periods of communication structures of CodePlex C # community based on large-scale data collections. Then we refine the concept of quantum mapping of a complex network; give the classification of the mapping, reveal that the quantum mapping in [ 18 – 20 ] is merely the simplest “structural mapping”; and define corresponding Hamiltonians and energy spectra of a complex network in different mappings. Afterwards we discuss why the quantum mapping of complex networks is necessary and point out the purpose of the mapping is to study the structural symmetry and symmetry breaking of networks according to the idea in quantum mechanism.…”

The scaling properties of dynamical fluctuations in temporal networks

“…It can be proved that F q can filter out the statistical fluctuations. The method of factorial moments has been applied analyze different complex systems, such as multiplicity of produced hadrons [11], human electroencephalogram and gait series in biology [12,13], financial price series [14], critical fluctuations in Bak-Sneppen model [18], spectra analysis of complex networks [15], to name a few. Specially it indicates that the fluctuations in the system have self-similarity when F q has a power-law dependence on the bin size M.…”

Synchrony and Asynchrony for Neuronal Dynamics Defined on Complex Networks

“…After it was shown that the connectivity of the Internet is well-described by "scale-free" graphs [10,11], there was an explosion of interest in the applied community to understand how complex networks can model natural systems [12], particularly in biology. The theory and simulation of dynamical systems defined on complex networks have been applied to ecology [13], neuroscience [14] and especially gene regulatory networks [15][16][17][18][19][20][21][22].…”