Juul Jonas S, Porter Mason A
Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen 2100-DK, Denmark.
Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095, USA.
Chaos. 2018 Jan;28(1):013115. doi: 10.1063/1.5017962.
Network structure can have a significant impact on the propagation of diseases, memes, and information on social networks. Different types of spreading processes (and other dynamical processes) are affected by network architecture in different ways, and it is important to develop tractable models of spreading processes on networks to explore such issues. In this paper, we incorporate the idea of synergy into a two-state ("active" or "passive") threshold model of social influence on networks. Our model's update rule is deterministic, and the influence of each meme-carrying (i.e., active) neighbor can-depending on a parameter-either be enhanced or inhibited by an amount that depends on the number of active neighbors of a node. Such a synergistic system models social behavior in which the willingness to adopt either accelerates or saturates in a way that depends on the number of neighbors who have adopted that behavior. We illustrate that our model's synergy parameter has a crucial effect on system dynamics, as it determines whether degree-k nodes are possible or impossible to activate. We simulate synergistic meme spreading on both random-graph models and networks constructed from empirical data. Using a heterogeneous mean-field approximation, which we derive under the assumption that a network is locally tree-like, we are able to determine which synergy-parameter values allow degree-k nodes to be activated for many networks and for a broad family of synergistic models.
网络结构会对疾病、模因以及社交网络上的信息传播产生重大影响。不同类型的传播过程（以及其他动态过程）受到网络架构的影响方式各不相同，因此开发易于处理的网络传播过程模型以探讨此类问题非常重要。在本文中，我们将协同作用的概念纳入网络上社会影响的两态（“活跃”或“被动”）阈值模型。我们模型的更新规则是确定性的，每个携带模因的（即活跃的）邻居的影响——取决于一个参数——可以根据节点活跃邻居的数量以一定量增强或抑制。这样一个协同系统对社会行为进行建模，其中采用的意愿会以一种取决于已采用该行为的邻居数量的方式加速或饱和。我们表明，我们模型的协同参数对系统动态有至关重要的影响，因为它决定了度为k的节点是否可能被激活。我们在随机图模型和根据经验数据构建的网络上模拟协同模因传播。使用我们在网络局部类似树状的假设下推导出来的非均匀平均场近似，我们能够确定对于许多网络和广泛的协同模型家族，哪些协同参数值允许度为k的节点被激活。
