Many optimization problems like domination and Steiner tree are NP-complete on chordal graphs but can be solved in polyno-mial time on doubly chordal graphs. Investigating properties of dou-bly chordal graphs probably help to design efficient algorithms for the graphs. We present some characterizations of dobly chordal graphs which are based on clique matrices and neighborhood matrics also men-tioned how a doubly perfect elimination ordering of a doubly chordal graph can be computed from the results.