As tools for teaching physical system modelling and simulation both the bond graph and graph-theoretic methods have clearly demonstrated value at undergraduate and graduate levels of education, and in applied industrial contexts. The very close connections between the two techniques give them various shared attributes in this respect, notably the three main virtues of physical analogy, capability for causal analysis and the cross-disciplinary universality of the energy flow representation. An outline is given of the main technical features, and how these relate to the pedagogical virtues, as well as an account of the complete technical equivalence of bond graphs and linear graphs as representations of a discrete physical system. Several important misconceptions about this relationship are discussed and clarified, including continued doubts about methodological equivalence, apparent differences that can be attributed to arbitrary formality and convention, and the non-use of some graph-theoretic equation formulation procedures with a bond graph model. Despite these facts, teaching experience has demonstrated that a degree of pedagogical asymmetry still exists between the bond graph and linear graph approaches. This situation is explained through differences in model symbolism and, in particular, as a consequence of following different pathways to arrive at the simultaneous port and terminal representations that characterize either model. The existence of an extensive resource of universal, flexible computer software for implementing and analysing bond graph physical system models is also an important factor which is not available for linear graph modelling, an important practical consideration that is likely to have curtailed the widespread use of the latter method in pedagogical situations.