The mathematical foundations of bond graphs—I. Algebraic theory

Abstract Elementary mathematical concepts from linear algebra are used to develop an independent theory for non-directed bond graphs. The definition of a bond graph is given and its structure as a combinatorial object is studied. This is accomplished by constructing a vector space, called the bond space of the bond graph. Topological information is encoded in the bond graph by defining a subspace of the bond space, the s -space. The internal bond information is eliminated by studying subspaces of the s -space, the cycle and internal space. A precise meaning is given to the association between bond graphs and linear graphs by comparing their respective cycle spaces. A technique, called the cut and paste method, is described which produces a bond graph associated with a given graph via its planar representation. Several problems associated with the inverse procedure are discussed.