Structural characteristics of the river network and its functional responses in the Haihe River basin based on small-world networks

River networks are channels for water flow within the hydrological cycle of a watershed, and their spatial evolution has significant impacts on watershed hydrological processes.Human modifications and reconstructions of river networks have significantly altered their topological structure and functionality.Analysing the structural characteristics and functional responses of evolving river networks is of great importance for their health assessment and management.This study proposes the concept of a "small-world river network" and constructs an assessment framework based on graph theory to analyse the structural characteristics, spatial growth patterns, and functional responses of an evolving river network.The results show that the current river network in the Haihe River basin exhibits small-world characteristics, such as high connectivity, large overall structure, and dense topology, and it shows high network efficiency.The development of the river network has scale-free characteristics, following a growth pattern of node increase and preferential connection, and it is constrained by spatial limitations imposed by "small-scale connections".Compared to the natural river network, the flood control function has increased by 65%, the water supply function has increased by 222%, and the ecological function has decreased by 78%, indicating a tendency towards non-uniform functional changes.The assessment results can provide technical support for the optimal management and planning of river networks in the watershed.