A simple approach for quantifying node centrality in signed and directed social

Wei-Chung Liu

Contact: wliu56@gate.sinica.edu.tw

The position of a node in a network can be defined and quantified in several ways, all informing about how the parts and the whole are related. Traditionally, node centrality can be defined by some combination of its local connectivity (degree) and non-local characteristics (distance). Here, we present a simple 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 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 network; while net effect describes, whether predominately positive or negative, the manner in which a node can exert on the 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.

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