By default, are two vertices in a graph allowed to have multiple edges connecting them, or does the graph specifically have to be classified as a multigraph in order for that to be true?
Here is the definition I am provided with by the Volume 2 book by AoPS:
A graph is a set of points, some of which are connected together by lines. ... The points of a graph are called its vertices, while the lines are called edges.
I suppose I would like to know what the definition of a graph is within the context of competitions such as the AMC and AIME.
Based on the comments I received and the knowledge I have gained in the past 6 months, a graph conventionally has at most 1 edge between any pair of vertices. Any graph with more than 1 such edge must be classified as a multigraph.