Delay effect in coevolutionary balance as a higher order interaction

Information propagation in network interactions is not an instant event but rather it is happening with a delay in real world. The evolution of network structure to reach to a balanced state in order to minimize the overall tensions is commonly considered without any delays but in fact the role of delay might influence when the network converts from the unbalanced to the balanced state. In this study we considered the coevolutionary balance model in which the interaction of both nodes and links in the network is taken into account and we assume that individuals are receiving the latest updated status of their neighbors with a specific delay. We have shown that this delay effect is equal to the appearance of the higher order interactions that are opposing the existing first order interaction in the simple coevolutionary balance without considering delay.