Toward uncertainty of weighted networks: An entropy-based model

Measuring the uncertainty is of both theoretical value and practical interest in the network science. The previous studies focus on measuring the uncertainty of the entire networks. However, how to measure the uncertainty of the individuals is still an open issue. To address this issue, the “asking for help” example is used to model the user behaviors. In this paper, we develop three heuristic rules to measure the utility of adjacent neighbors to each node in the networks. Then, the fuzzy systems theory is used to convert the utility of each neighbor into the membership functions. Next, we derive the uncertainty of each node based on the Shannon entropy. Our result demonstrates the overall uncertainty of the networks, and also the uncertainty for the individual node. Moreover, our model also reflects the uncertainty of nodes for choosing to strengthen or weaken the existed links between their neighbors with the evolution of networks. Instead of forming new links but changing the existed relationship between nodes, we consider the proposed uncertainty measure may suggest a crucial property of the networks on the opposite side of link prediction.