"using relations" or a particular data structure wasn't at all the point of this particular discussion. The point was that, for a simple directed graph, the ed

"using relations" or a particular data structure wasn't at all the point of this particular discussion. The point was that, for a simple directed graph, the edges represent a binary relationship. While for a weighted directed graph, it represents a relationship-matrix. For the graph being non-directed this would mean, that the relationship(-matrix) is symmetric. Meaning that any algebra, algorithm, proof, etc. on graphs of that type can be applied for the other interpretation as well. Implementation is a different question. "Most" binary relations we happen upon (less-than as the obvious) have an infinite domain and infinite cardinality (when represented as a set of tuples), making it very hard to "visualize" as a graph.