It has been a significant and challenging issue to derive the complex valid contracted graphs (CGs) with hexagonal links plus other links and identify their isomorphism for creating novel closed mechanisms. This paper focuses on the derivation of the valid CGs with hexagonal links plus other links using the characteristic strings (CSs). First, the concepts on the CGs and CSs are explained, and the numbers of vertices and edges in the CGs are solved. Second, the relative criterion are determined for representing/deriving CGs and identifying isomorphic/invalid CGs by CSs. Third, some simple CGs are derived from some associated linkages with hexagonal links plus more other links, are represented by CSs, and the isomorphic/invalid CGs are identified using the CSs and the isomorphic queues of the links. Fourth, some examples are given for illustrating their applications. Finally, many complex valid CGs with more hexagonal links plus other links are represented and derived using CSs, and their isomorphism are identified using CSs.