Spectra of random networks with arbitrary degrees
Spectra of random networks with arbitrary degrees
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DOI：
10.1103/physreve.99.042309
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发表时间：
2019-01
期刊：
影响因子：
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通讯作者：
M. Newman;Xiao Zhang;R. Nadakuditi
中科院分区：
文献类型：
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作者：
M. Newman;Xiao Zhang;R. Nadakuditi
我们导出了计算局部树状网络谱的消息传递方法及其近似，它允许我们计算具有任意结点度的随机图的谱密度的闭式表达式或快速数值逼近--所谓的构型模型。我们发现，除了最稀疏的网络之外，后一种近似对所有网络都很有效。我们还导出了谱的带边位置的界限，这对于识别网络中的结构相变是重要的。
We derive a message-passing method for computing the spectra of locally treelike networks and an approximation to it that allows us to compute closed-form expressions or fast numerical approximates for the spectral density of random graphs with arbitrary node degrees-the so-called configuration model. We find that the latter approximation works well for all but the sparsest of networks. We also derive bounds on the position of the band edges of the spectrum, which are important for identifying structural phase transitions in networks.