社交网络影响博弈的权力指数与新的中心性测度
Power indices of influence games and new centrality measures for social networks
摘要：
在社会网络分析中，有一种普遍的看法，即影响力与决定社会的全球行为有关，因此它可以用来通过针对适当的初始个体集来加强合作，或者分析全球选择过程。在这里，我们提出了中心性的措施，可以用来分析相关的影响力传播过程中的演员的相关性。在[39]中，它被认为是一个多智能体系统，其中智能体渴望根据对其他个体执行任务的意愿的感知来执行集体任务。该设置使用称为影响力游戏的简单游戏的概念建模。这些游戏是在图上定义的，其中节点由其影响力阈值标记，节点之间的影响力传播用于确定联盟是否获胜。影响力博弈提供了通过经典的权力指数来衡量社会网络中参与者的重要性的工具，并提供了一个考虑新的中心性标准的框架。在本文中，我们考虑了两个最经典的幂指数，即，Banzhaf和Shapley-Shubik指数作为影响力博弈中社交网络的中心性度量。虽然有一些工作与博弈论网络的特定场景相关，但在这里，我们使用这些指数作为任何社交网络中的中心性度量，其中可以应用影响力传播现象。此外，我们定义了新的中心性度量，如满意度和努力度，据我们所知，到目前为止还没有考虑过。我们还进行了比较的建议措施与其他三个经典的中心性措施，度，接近度和介数，考虑三个社交网络。我们表明，在某些情况下，我们的测量提供类似于其他措施的中心层次结构，而在其他情况下，提供不同的层次结构。
英文摘要：
In social network analysis, there is a common perception that influence is relevant to determine the global behavior of the society and thus it can be used to enforce cooperation by targeting an adequate initial set of individuals or to analyze global choice processes. Here we propose centrality measures that can be used to analyze the relevance of the actors in process related to spread of influence. In [39] it was considered a multiagent system in which the agents are eager to perform a collective task depending on the perception of the willingness to perform the task of other individuals. The setting is modeled using a notion of simple games called influence games. Those games are defined on graphs were the nodes are labeled by their influence threshold and the spread of influence between its nodes is used to determine whether a coalition is winning or not. Influence games provide tools to measure the importance of the actors of a social network by means of classic power indices and provide a framework to consider new centrality criteria. In this paper we consider two of the most classical power indices, i.e., Banzhaf and Shapley-Shubik indices, as centrality measures for social networks in influence games. Although there is some work related to specific scenarios of game-theoretic networks, here we use such indices as centrality measures in any social network where the spread of influence phenomenon can be applied. Further, we define new centrality measures such as satisfaction and effort that, as far as we know, have not been considered so far. We also perform a comparison of the proposed measures with other three classic centrality measures, degree, closeness and betweenness, considering three social networks. We show that in some cases our measurements provide centrality hierarchies similar to those of other measures, while in other cases provide different hierarchies.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
