论文标题
卡利树的雪崩大小分布
Avalanche-size distribution of Cayley tree
论文作者
论文摘要
在开发网络中消除恶意现象的差异（例如流行病和伪造信息）的策略方面，对网络的攻击是一个非常重要的问题，该网络通常在研究网络免疫中命名。 The traditional approach of evaluating the effectiveness of attacks on networks, is focused on measuring some macro parameters related to an entire attack, such as the critical probability of a percolation occurrence in the network $p_c$ and the relative size of the largest component in the network - the giant component, but not considering the attack on a micro perspective, which is the analysis of the node removals, during an attack, themselves, their characteristics and results.在本文中，我们介绍并采用了最后一个专注于攻击的微观量表的方法。基于网络中的渗透理论，我们分析了由于从网络中删除单个节点而导致的雪崩结果的现象，在该状态下，一个状态属于一个节点属于网络的巨型组件属于其他节点，导致其他节点也导致其与片段的贡献更大的贡献（这是对片段化的贡献）的贡献（免疫量）。具体来说，我们将自己集中在雪崩大小的参数上，这是由于单个节点去除而与巨型组件断开的节点的数量。关于在Cayley树类型的网络上随机攻击，我们通过分析得出整个攻击过程中的雪崩大小的分布，直到拆除网络（免疫）并终止攻击为止。
Attacks on networks is a very important issue in developing strategies of eradicating spreads of malicious phenomena in networks, such as epidemics and fake information, which are generally named in the research networks immunization. The traditional approach of evaluating the effectiveness of attacks on networks, is focused on measuring some macro parameters related to an entire attack, such as the critical probability of a percolation occurrence in the network $p_c$ and the relative size of the largest component in the network - the giant component, but not considering the attack on a micro perspective, which is the analysis of the node removals, during an attack, themselves, their characteristics and results. In this paper we present and apply the last method of focusing on the micro scale of an attack. Based on the theory of percolation in networks, we analyze the phenomenon of an avalanche results due to a single node removal from a network, that is a state in which a removal of one node belongs to the network's giant component causes other nodes to be also disconnected from it, which is a much greater contribution to the fragmentation (immunization) of the network than only the single original node removal itself. Specifically, we focus ourselves on the parameter of the size of an avalanche, which is the number of nodes that are disconnected from the giant component due to a single node removal. Relating to a random attack on a network of the type of Cayley tree, we derive analytically the distribution of the sizes of avalanches occur during the entire attack on it, until the network is dismantled (immunized) and the attack is terminated.
