Analysis of complex contagions in random multiplex networks
Analysis of complex contagions in random multiplex networks
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DOI：
10.1103/physreve.86.036103
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发表时间：
2012-04
期刊：
影响因子：
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通讯作者：
Osman Yağan;V. Gligor
中科院分区：
文献类型：
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作者：
Osman Yağan;V. Gligor
我们研究随机多重网络中影响力的扩散，其中链接可以有 r 种不同类型，并且对于给定的内容（例如谣言、产品或政治观点），每种链接类型都与 [0,∞] 中的内容相关参数 ci 相关联，该参数测量 i 个链接在传播该内容时的相对偏差类型。在这种情况下，我们提出了一种传染的线性阈值模型，其中如果节点“感知”的活跃邻居比例超过阈值τ，则节点会切换状态。即，如果 Σcimi/Σciki 超过其阈值 τ，则通过类型 i 链路连接到 mi 个活动邻居和 ki-mi 个不活动邻居的节点将变为活动状态。在这个模型下，我们获得了全球传播事件的条件、概率和预期规模。我们的结果在多个方向上扩展了复杂传染的现有工作，通过（i）为顶点既不相同也不不相交的耦合随机网络提供解决方案，（ii）强调内容对复杂传染动态的影响，以及（iii）表明多路网络上的内容相关传播导致图的巨大脆弱部分与全局级联条件之间的微妙关系，这在文献中的现有模型中是看不到的。
We study the diffusion of influence in random multiplex networks where links can be of r different types, and, for a given content (e.g., rumor, product, or political view), each link type is associated with a content-dependent parameter ci in [0,∞] that measures the relative bias type i links have in spreading this content. In this setting, we propose a linear threshold model of contagion where nodes switch state if their "perceived" proportion of active neighbors exceeds a threshold τ. Namely a node connected to mi active neighbors and ki-mi inactive neighbors via type i links will turn active if ∑cimi/∑ciki exceeds its threshold τ. Under this model, we obtain the condition, probability and expected size of global spreading events. Our results extend the existing work on complex contagions in several directions by (i) providing solutions for coupled random networks whose vertices are neither identical nor disjoint, (ii) highlighting the effect of content on the dynamics of complex contagions, and (iii) showing that content-dependent propagation over a multiplex network leads to a subtle relation between the giant vulnerable component of the graph and the global cascade condition that is not seen in the existing models in the literature.