Impact of delay on the formation of high-order interactions and structural imbalance

In real systems, information is never delivered quickly and always will spread with a delay. Because of this delay, an event from the past influences the activities of another entity today, which is no guarantee of direct contact between the two. In certain ways, this can be the result of high-order interactions in which a direct connection is not always formed. In this paper, we look at how this delay affects the dynamics of Heider balance theory. We demonstrate that Heider balance with a delay as a third-order interaction is equivalent to fourth-order interactions or higher order but without the delay. Higher-order interaction is required by raising the value of delay. Our finding indicates that in the dynamics of Heider balance, increasing the delay period increases the order of interactions and the presence of imbalanced triangles even at temperatures close to zero.