AI 中文总结
该研究在有向加权网络中，对比ISM三种概率中心性与常用中心性，发现标准中心性可近似广播影响，但常遗漏接收影响及概率中介的细微特征。
AI 中文摘要
影响传播模型（ISM）提出了三种概率中心性度量：出中心性、入中心性和ISM介数中心性。出中心性衡量一个节点影响其他节点的平均概率，入中心性衡量其他节点影响该节点的平均概率，ISM介数中心性衡量移除某个节点后总概率影响的变化。这些度量依赖边的传播概率，且允许游走至指定的最大长度。我们在有向加权网络中，将ISM中心性度量与常用的加权变体出度、入度、 closeness（接近中心性）、最短路径介数及Katz中心性进行比较，使用了四个真实世界在线社交网络，以及由Erdős-Rényi、可导航小世界和有向无标度模型生成的九个合成网络。对于合成网络，边概率来自三种beta分布。我们使用皮尔逊相关系数和斯皮尔曼秩相关系数评估中心性数值及其排序的相似性。结果显示，ISM出中心性与加权出度、外向Katz中心性之间存在强相关性，尤其在边概率较低时；相反，ISM入中心性与其他度量的关系随网络拓扑变化，有时会产生负相关。ISM介数与最短路径介数之间的相关性也依赖拓扑，且当替代影响路径变得更相关时会减弱。总体而言，标准中心性度量可近似广播影响的作用，但往往会遗漏接收影响和概率中介角色的细微差别。
英文摘要
The Influence-Spreading Model (ISM) introduces three probabilistic centrality measures: out-centrality, in-centrality, and ISM betweenness centrality. Out-centrality measures the average probability that a node influences others, while in-centrality measures the average probability that others influence a node. ISM betweenness centrality measures the change in total probabilistic influence when a node is removed. These measures depend on edge transmission probabilities and allow walks up to a specified maximum length. We compare the ISM centrality measures to commonly used weighted variants of out-degree, in-degree, closeness, shortest-path betweenness, and Katz centrality in directed, weighted networks using four real-world online social networks and nine synthetic networks generated by Erdős-Rényi, navigable small-world, and directed scale-free models. For the synthetic networks, the edge probabilities are drawn from three beta distributions. We evaluate the similarity in centrality values and their ranking using Pearson correlation and Spearman's rank correlation coefficients. Results show strong correlations between the ISM out-centrality and weighted out-degree and outward Katz centrality, particularly for low edge probabilities. Conversely, relationships between the ISM in-centrality and other measures vary with network topology, sometimes yielding negative correlations. Correlations between the ISM betweenness and the shortest-path betweenness are also topology-dependent and weaken as alternative influence paths become more relevant. Overall, standard centrality measures can approximate the influence of broadcasting influence but often miss the nuances of receiving influence and probabilistic intermediary roles.
