无标度结构有多鲁棒？攻击下优先连接模型的相变
How Robust is Scale-Free Structure? Phase Transitions in Preferential Attachment Model under Attack?
- Cornell University（康奈尔大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文研究攻击者干扰优先连接网络增长时的相变现象，发现攻击技能低于临界值时网络保持无标度结构，高于临界值时该结构被破坏，并分析了度分布尾部行为。
中文摘要 AI 辅助
攻击网络是否会对其结构产生重大影响？在本工作中，我们通过研究一个动态的优先连接型图来探讨这一问题，在该图中，攻击者干扰网络的增长机制。我们表明，我们的攻击模型表现出相变现象。若攻击者的技能较低，网络将保留其从底层优先连接结构继承而来的无标度结构（尽管由于攻击，度分布的尾部会变轻）。当攻击者的技能增加并跨越临界边界时，无标度性质被破坏。攻击者的技能表示为在给定步骤中，攻击者成功阻止向网络添加边，并反而（以优先方式）导致一条边被删除的概率。在所有情况下，我们都描述了度分布的尾部行为。
英文摘要
Will an attack on a network affect its structure in a major way? In this work we study this question by investigating a dynamic preferential attachment-type graph in which an attacker interferes with the growth mechanism. We show that our model of an attack exhibits a phase transition. If the skill of the attacker is low, the network preserves its scale-free structure inherited from the underlying preferential attachment structure (even though the tail of the degree distribution becomes lighter due to the attack). When the skill of the attacker increases and crosses a critical boundary, the scale-free property is destroyed. The skill of the attacker is expressed as the probability that, at a given step, the attacker succeeds in preventing adding an edge to the network and, instead, causes a deletion (in a preferential manner) of an edge. In all cases we describe the tail behaviour of the degree distribution.
