each sample path, we need to specify the infection time and recovery time for each healthy node and the infection time for each infected node, so the number of possible sample paths is at the order of $\Omega(t^N),$ where $N$ is the network size and $t$ is the time the snapshot is obtained. Therefore, the MLE problem is difficult to solve even when $t$ is known. The problem becomes much harder when $t$ is unknown, which is the assumption of this paper. To overcome this difficulty, we propose a sample path based approach. We propose to find the sample path which most likely leads to the observed snapshot and view the source associated with that sample path as the information source. We call this problem optimal sample path detection problem. We investigate the structure properties of the optimal sample path in trees. Defining the infection eccentricity of a node to be the maximum distance from the node to infected nodes, we prove that the source node of the optimal sample path is the node with the minimum infection eccentricity. Since a node with the minimum eccentricity in a graph is called the Jordan center, we call the nodes with the 