Jalan Sarika
Max-Planck Institute for the Physics of Complex Systems, Dresden, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 2):046101. doi: 10.1103/PhysRevE.80.046101. Epub 2009 Oct 1.
We study spectral behavior of sparsely connected random networks under the random matrix framework. Subnetworks without any connection among them form a network having perfect community structure. As connections among the subnetworks are introduced, the spacing distribution shows a transition from the Poisson statistics to the Gaussian orthogonal ensemble statistics of random matrix theory. The eigenvalue density distribution shows a transition to the Wigner's semicircular behavior for a completely deformed network. The range for which spectral rigidity, measured by the Dyson-Mehta Delta3 statistics, follows the Gaussian orthogonal ensemble statistics depends upon the deformation of the network from the perfect community structure. The spacing distribution is particularly useful to track very slight deformations of the network from a perfect community structure, whereas the density distribution and the Delta3 statistics remain identical to the undeformed network. On the other hand the Delta3 statistics is useful for the larger deformation strengths. Finally, we analyze the spectrum of a protein-protein interaction network for Helicobacter, and compare the spectral behavior with those of the model networks.
我们在随机矩阵框架下研究稀疏连接随机网络的谱行为。彼此之间没有任何连接的子网络形成具有完美社区结构的网络。随着子网络之间连接的引入，间距分布呈现出从泊松统计到随机矩阵理论的高斯正交系综统计的转变。对于完全变形的网络，特征值密度分布呈现出向维格纳半圆行为的转变。由戴森 - 梅塔Delta3统计量测量的谱刚性遵循高斯正交系综统计的范围取决于网络相对于完美社区结构的变形。间距分布对于追踪网络相对于完美社区结构的非常微小的变形特别有用，而密度分布和Delta3统计量与未变形网络保持相同。另一方面，Delta3统计量对于较大的变形强度是有用的。最后，我们分析了幽门螺杆菌的蛋白质 - 蛋白质相互作用网络的谱，并将谱行为与模型网络的谱行为进行比较。
