Ties in Overlapping Community Structures: Strong or Weak?

In recent years, the identification and application of strong and weak ties in social networks has drawn increasing attention. The traditional definitions of strong ties (with two endpoints in the same community) and weak ties (with two endpoints in different communities) are being challenged by overlapping community structures. Because of their unique nature, the relationships between overlapping nodes and non-overlapping nodes are difficult to classify as strong or weak. In view of this, it is here proposed that the coefficient indicator for overlapping communities was used to redefine node relationships and enable the quantification of strong and weak ties. Next, changes in the quantities of strong and weak ties were analyzed by varying the threshold values of the overlap coefficient. Finally, the effect of weak ties in information dissemination was assessed in overlapping and non-overlapping situations, respectively. Results demonstrated that the overlap coefficient proposed in this paper could better characterize the strong and weak attributes of edges under overlapping community structures.