Triplet Evolution

We study the evolution of networks through `triplets' -- three-node graphlets. We develop a method to compute a transition matrix of these triplets to describe their evolution in temporal networks. To identify the network dynamics' non-pairwise interactions, we compare both artificial and real-world data to a pairwise interaction model. The significant differences between the computed matrix and the calculated matrix from the fitted parameters demonstrate that non-pairwise interactions exist for various real-world data sets. Furthermore, different entries of the matrix differences reveal the real-world systems have different higher-order interaction patterns which are seldomly reported in the previous researches. We then use these transition matrices as the basis of a link prediction algorithm. We investigate our algorithm's performance on four temporal networks comparing our approach against ten other link prediction methods. Our results show that higher-order interactions play a crucial role in the evolution of networks as we find our method along with two other methods based on non-local interactions, give the best overall performance. The results also confirm the concept that the higher-order interaction patterns, i.e., triplet dynamics, can help us understand and predict different real-world systems' evolution.