What are the rules for plotting directed graphs?

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Say I have an ordered pair of sets. One contains the vertices and the other - edges.

What are the rules for actually plotting the graphs with these givens? Can a graph be plotted differently given the same set of vertices and same set of edges?

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There are no rules for plotting graphs. As long as you have a dot for each vertex and a line for each edge, and the edges connect the appropriate vertices as indicated by the edge set of the graph, it doesn't matter how the graph is drawn.