We examine two-layer networks and centrality measures defined on them. The propose two fast and accurate algorithms to approximate the game-theoretic centrality measures and examine connection between centrality measures and characteristics of opinion dynamic processes on such networks. As an example, we consider a Zachary's karate club social network and extend it by adding the second (internal) layer of communication. Internal layer represents the idea that individuals can share their real opinions with their close friends. The structures of the external and internal layers may be different. As characteristics of of opinion dynamic processes we mean consensus time and winning rate of a particular opinion. We find significantly strong positive correlation between internal graph density and consensus time, and significantly strong negative correlation between centrality of authoritative nodes and consensus time.

翻译：本文研究双层网络及其上定义的中心性度量。我们提出了两种快速且精确的算法来近似博弈论中心性度量，并探讨了此类网络中中心性度量与观点动态过程特性之间的关联。以Zachary空手道俱乐部社交网络为例，我们通过添加第二层（内部）通信网络对其进行扩展。内部层体现了个人可与亲密朋友分享真实观点的理念。外部层与内部层的结构可能不同。作为观点动态过程的特征，我们关注共识达成时间与特定观点的获胜率。研究发现，内部图密度与共识时间呈显著强正相关，而权威节点的中心性与共识时间呈显著强负相关。