Fig. 1: Elementary decomposition of undirected hyperedges.
From: Synchronization induced by directed higher-order interactions
An undirected 2-hyperedge can be seen as the composition of three directed hyperedges. In each of the three directed 2-hyperedges, the nodes acting as source of the interaction are interchangeable, i.e., switching them does not alter the nature of the interaction. Therefore, the adjacency tensors A(2) is symmetric to a permutation of the indices corresponding to the source nodes.
