The position of a node in a social network, or node centrality, can be quantified in several ways. Traditionally, it can be defined by considering the local connectivity of a node (degree) and some non-local characteristics (distance). Here, we present an approach that can quantify the interaction structure of signed digraphs and we define a node centrality measure for these networks. The basic principle behind our approach is to determine the sign and strength of direct and indirect effects of one node on another along pathways. Such an approach allows us to elucidate how a node is structurally connected to other nodes in the social network, and partition its interaction structure into positive and negative components. Centrality here is quantified in two ways providing complementary information: total effect is the overall effect a node has on all nodes in the same social network; while net effect describes, whether predominately positive or negative, the manner in which a node can exert on the social network. We use Sampson’s like-dislike relation network to demonstrate our approach and compare our result to those derived from existing centrality indices. We further demonstrate our approach by using Hungarian school classroom social networks.

中文翻译：

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一种简单的量化签名和定向社交网络中节点中心性的方法

节点在社交网络中的位置或节点中心性可以通过几种方式进行量化。传统上，可以通过考虑节点的本地连接性（度）和一些非本地特征（距离）来定义。在这里，我们提出了一种可以量化有向图的相互作用结构的方法，并为这些网络定义了节点中心度度量。我们方法背后的基本原理是确定一个节点沿着路径对另一个节点的直接和间接影响的符号和强度。这种方法使我们能够阐明一个节点如何在结构上连接到社交网络中的其他节点，并将其交互结构划分为积极和消极的组成部分。可通过两种提供补充信息的方式来量化中心性：总效果是节点对同一社交网络中所有节点的总体影响；而净效应主要是正面的或负面的描述了节点在社交网络上发挥作用的方式。我们使用桑普森的“喜欢/不喜欢”关系网络来演示我们的方法，并将我们的结果与从现有集中度指标得出的结果进行比较。我们通过使用匈牙利学校课堂社交网络进一步展示了我们的方法。