Deployment of portable access points (APs) in disaster affected areas has been heralded by many contemporary researchers as a key technique to formulate disaster recovery networks. However, existing research works do not effectively address one of its key problems, i.e., the low capacity of the backbone network (constructed by the APs) which is unable to satisfy the high user demands emanating from the users in the local network of each AP. We consider cooperative communications to be a promising candidate to alleviate this problem, and formulate the trade-off relationship between the gained throughput and the network complexity. Also, we propose a novel graph-based topology control algorithm to solve the problem by exploiting cooperative communications to increase the inter-AP throughput gain. We first model the network by using a logical graph, where any two nodes are connected by a logical link if they are within the transmission range of each other. After that, k best paths, in terms of throughput gain, via mobile terminals, are found to connect any pair of APs. The constructed topology based on the resulted paths is used for cooperative communications. An in-depth analysis of the effect of the value of k on the network complexity and throughput gain is presented. Also, by introducing cooperative throughput gain speed as the utility of our proposal, we prove that there is an optimal value of k that maximizes the utility. Furthermore, extensive simulations are conducted to validate the analytical findings and demonstrate the effectiveness of our proposal.