Random networks are heterogeneous exhibiting a multi-scaling law
Random networks are heterogeneous exhibiting a multi-scaling law
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随机网络是异构的，表现出多尺度规律
DOI：
10.1016/j.physa.2021.126479
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发表时间：
2021-10-23
影响因子：
3.3
通讯作者：
Miao，Qiguang
中科院分区：
文献类型：
--
作者：
Sun，Peng Gang;Che，Wanping;Miao，Qiguang
与无标度结构(SF)不同，Erdos-Renyi(ER)的随机网络也被称为由同类节点组成的同构网络，因为这些节点近似具有相同的度，服从泊松分布。本文试图证明这个随机网络实际上是异质的，即，它是由不同类型的节点组成的，通过引入一个新的度量，称为B-指数来量化节点，该度量定义为节点的移除可以破坏其邻域的程度。在随机网络上观察到一个有趣的现象，即B指数的分布可以粗略地划分为许多不同尺度的子分布，表现出多尺度规律。这种现象随着随机网络的变化而出现、波动和消失。此外，对易感感染恢复(SIR)模型的传播动力学分析表明，B指数最高的节点可以缓解多个疫源地的重叠问题，对流行病的传播影响更大，特别是对于较少的疫源地。
Unlike the scale-free (SF) architecture, random networks of the Erdos–Renyi (ER) are also called homogeneous networks consisting of the same kind of nodes because these nodes approximately have same degrees, which follow a Poisson distribution. This paper tries to demonstrate that this random network is actually heterogeneous, ie, it is composed of different kinds of nodes by introducing a new metric, called B-index to quantify a node, defined as the extent that the node’s removal can break down its neighborhood. One interesting phenomenon is observed on random networks, ie, the distribution of B-index can be roughly divided into many sub-distributions with different scalings exhibiting a multi-scaling law. This phenomenon appears, fluctuates and disappears as the changes of random networks. In addition, the analysis of spreading dynamics on the susceptible infected recovered (SIR) model suggests that the nodes with the highest B-index can alleviate the overlap problem of infected area of multiple origins, and are more influential for the spreading of epidemics, especially for the small number of origins.