Modeling data-driven adaptive distributionally robust equilibrium last mile relief network under centrality metric

•An original centrality metric objective function for the LMRNP is introduced.•A new data-driven adaptive distributionally robust equilibrium programming method.•The DBSCAN algorithm is newly adopted to construct a data-driven ambiguity set.•The proposed model is theoretically derived into a computationally solvable form.•The performance of the deduced model is validated by two real data sets.