In this paper, a distributed secure state estimation problem that is state estimation in distributed observer system in the presence of attacks is mainly discussed. We introduce the notion of graph-based distributed observer representation, virtual state, and a subgroup to derive a condition for the secure state estimation. By the graph-based distributed observer representation, we can consider the system's observability and communication pass connectivity as graph connectivity at once. With the notion of virtual state and the subgroup, we derive the state estimation condition which is the inequality relationship between the number of the allowable attacked observer and the graph connectivity as a theorem. Finally, a simple numerical example verifies the theorem.