Distributed denial of service, DDoS, attacks are drastically increasing, therefore, they cause serious threats for information networks. This paper proposes, for the first time, the use of a graph theoretic approach to exploit the entropy techniques for detecting and tracing back DDoS attackers. It presents a novel approach to traceback DDoS attacks using modified Floyd-Warshall algorithm, TDA/MFWA. Such model starts by feeding the network adjacency matrix in which the link weights are changed to comply with the network traffic entropy, accordingly the reachability from node to node can be examined. Then we borrowed the idea of enumerating all the intermediate points between every pair of network nodes from Floyd-Warshall algorithm and modified it to find out the victim node(s). The fact that entropy at network nodes is systematically accounted using a modified Floyd-Warshall algorithm contributes to the smartness and dependability of TDA/MFWA.