Higher-order network

A higher-order Markov chain model can be viewed as a memoryless Random walk in the k-th order network $$G^k = (V^k, E^k),$$ where each node $(v_1, \dots, v_k) \in V^k$ is connected by k-th order link. For instance, when $k=2$, it is like considering each edge as a node and considering link->link transition (cf. Non backtracking matrix and Link community). See also Rosvall2014memory.

Rosvall & Lambiotte paper

• From networks to optimal higher-order models of complex systems

Pham2022empirical may provide an argument against using higher-order network models.

Quanta magazine had an article How Big Data Carried Graph Theory Into New Dimensions.