The spread of ideas in a weighted threshold network

A threshold network is a type of complex network that is useful to model the way in which ideas travel through a human population. Each node has a threshold and only activates if it receives a number of inputs equal to or above the threshold. We build upon work that uses simple distributions of degrees and thresholds by introducing a weighting factor that assigns edges to nodes based on distance apart and similarity of thresholds. This models the way in which people tend to associate more with people of similar beliefs and those who live closer geographically. The model we develop agrees with simulations when the standard deviation of the threshold distribution is low