Although the importance of Disaster Response Networks (DRNs) has been highlighted in many researches, the requirement of spectrum agility has not been well addressed. In this paper, we focus on using all-spectrum cognitive radio for DRNs to fulfill this requirement. We consider a DRN constructed by Cognitive Radio Base Stations (CRBSs), which are deployed in the disaster affected area. Each CRBS is equipped with multiple antennas to support different frequency bands available in the area. Based on the considered DRN, we propose a Graph-based Hybrid Adaptive Routing scheme, which we refer to as GHAR. There are two phases in GHAR, centralized phase for topology formation and distributed phase for adaptive routing. In the centralized phase, we propose an algorithm that unites k non-overlapping minimum spanning trees to construct the topology for the next phase. We provide an analysis on the relationship between k and the adaptability with cognitive radio as well as the complexity of routing process. We also provide an analysis on the optimality of k. Furthermore, extensive simulations are conducted to validate our analysis. Simulation results confirm the effectiveness of our proposal and the existence of the optimal value of k.