This contribution explores the teaching of graph theory in the context of engineering education. We examine how teachers use collectively designed resources in terms of their backgrounds. After a literature review, we justify the choice to develop an analytical framework for studying the materials in terms of connections to be established in the resources. We suggest developments around the theoretical concept of connectivity, which allows us to analyze the potential connectivity, characterized by the connections enabled by the resources for teaching; and the effective connectivity that develops in teachers' practices and during the implementation of resources. We study the effective connectivity in terms of each teacher's personal relationship with graph theory. Graph theory evolves at the interface of mathematics and computer science research. We consider the case of two teachers, a computer scientist and a mathematician in a French Engineering School in France. The data collected consists of resources for teaching graph theory in engineering courses and interviews with teachers. As for results, we characterize how forms of connectivity developed in the use of resources for teaching graph theory are largely determined by the teachers' backgrounds.