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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.

Human is a highly cultural species with diversified skills and knowledge. In this paper, we examine whether the diversification of skills and knowledge can promote the emergence of social ties between individuals as means for acquiring resources. Specifically, we construct a simulation model consisting of two types of actors—one who uses social ties to search for resources and one who does not—and allow them to compete for resources that are distributed in resource patch networks of varying structures. In a densely connected resource patch network, implying a setting with less diversified sets of skills and knowledge, model result demonstrates that social ties can be detrimental to those adopting it. In a sparsely connected network, implying a setting with more diversified sets of skills and knowledge, social-type strategy can outcompete solitary-type strategy. Furthermore, actors with a pure social-type strategy are always inferior to their solitary competitors, regardless the structure of the resource patch network. Our modeling framework is of a very fundamental nature, and its relevance to existing theories and the sociological implication of its results are discussed.