Kühn Reimer, van Mourik Jort
Mathematics Department, King's College London, Strand, London WC2R 2LS,United Kingdom.
NCRG, Aston University, Aston Triangle, Birmingham B4 7ET, United Kingdom.
Phys Rev E. 2020 Sep;102(3-1):032302. doi: 10.1103/PhysRevE.102.032302.
We investigate the heterogeneity of outcomes of repeated instances of percolation experiments in complex networks using a message-passing approach to evaluate heterogeneous, node-dependent probabilities of belonging to the giant or percolating cluster, i.e., the set of mutually connected nodes whose size scales linearly with the size of the system. We evaluate these both for large finite single instances and for synthetic networks in the configuration model class in the thermodynamic limit. For the latter, we consider both Erdős-Rényi and scale-free networks as examples of networks with narrow and broad degree distributions, respectively. For real-world networks we use an undirected version of a Gnutella peer-to-peer file-sharing network with N=62568 nodes as an example. We derive the theory for multiple instances of both uncorrelated and correlated percolation processes. For the uncorrelated case, we also obtain a closed-form approximation for the large mean degree limit of Erdős-Rényi networks.
我们使用一种消息传递方法来研究复杂网络中渗流实验重复实例结果的异质性，以评估属于巨型或渗流簇的异质、节点相关概率，即大小与系统大小呈线性比例的相互连接节点的集合。我们针对大型有限单实例以及热力学极限下配置模型类中的合成网络来评估这些概率。对于后者，我们分别将厄多斯 - 雷尼网络和无标度网络视为度分布窄和宽的网络示例。对于真实世界的网络，我们以具有N = 62568个节点的Gnutella对等文件共享网络的无向版本为例。我们推导了不相关和相关渗流过程的多个实例的理论。对于不相关的情况，我们还获得了厄多斯 - 雷尼网络大平均度极限的闭式近似。
