Advancing evolution characterization in dynamic networks: A quantum walk and thermodynamics perspective

Dynamic networks are useful models for representing changing systems, such as social and trading networks. Accurately characterizing the evolution states of these networks is crucial for effective representation learning and future link prediction. However, existing methods struggle to distinguish between similar local evolution states, providing the same embedding for nodes in similar but distinct local graph topologies. In addition, previous methods fail to capture the change of overall topology over time, i.e. global evolution state, which limits these methods to a local or static structure. To address these limitations, we propose a novel framework called EANQWT ( E volution A ware N etwork with Q uantum W alk and T hermodynamics). During the encoding phase, the framework utilizes the average results of continuous-time quantum walks as quantum migration probabilities to differentiate between similar local evolution states. Additionally, EANQWT integrates an innovative Multi-view Thermodynamic Mixture of Experts (MTMoE) decoder, which considers quantum thermodynamic temperatures, a measurement of changes in the entire graph, from multiple perspectives to determine the existence of links between nodes. Our experimental results in both transductive and inductive settings show that EANQWT either surpasses or matches various state-of-the-art baselines. • The quantum walk-based method is used to measure importance between nodes. • Results of quantum walks can separate similar topology in dynamic networks. • Quantum thermodynamic temperatures can represent evolution of dynamic networks. • Temperatures observed from various perspectives shape the global evolution state.