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GraphPlot

Draws a graph given as a list of edges.

$ wo 'Head[GraphPlot[{1 -> 2, 2 -> 3, 3 -> 1}]]'
Graphics

A square matrix is taken directly as an adjacency matrix — symmetric matrices give undirected edges, anything else gives directed edges:

$ wo 'Head[GraphPlot[{{0, 1, 0}, {1, 0, 1}, {0, 1, 0}}]]'
Graphics

$ wo 'Head[GraphPlot[{{0, 1, 0}, {0, 0, 1}, {1, 0, 0}}]]'
Graphics

Method names the embedding to lay the vertices out with — "CircularEmbedding" puts all of them on one circle, even when the graph falls apart into separate pieces:

$ wo 'Head[GraphPlot[{1 -> 2, 3 -> 4}, Method -> "CircularEmbedding"]]'
Graphics

EdgeShapeFunction -> f draws each edge with f[{pt, …}, edge] instead of the built-in arrow. The second argument is the edge itself, so a DirectedEdge rather than a plain pair of vertices:

$ wo 'Head[GraphPlot[{1 -> 2, 2 -> 3}, EdgeShapeFunction -> ({Blue, Dashed, Line[#1]} &)]]'
Graphics

$ wo 'Head[GraphPlot[{1 -> 2, 2 -> 3}, EdgeShapeFunction -> (If[MemberQ[{DirectedEdge[1, 2]}, #2], {Blue, Arrow[#1]}, {LightGray, Line[#1]}] &)]]'
Graphics

EdgeShapeFunction -> None leaves the edges undrawn, a shape name says how to draw them without a function, and the rule form gives single edges a shape of their own:

$ wo 'Head[GraphPlot[{1 -> 2, 2 -> 3}, EdgeShapeFunction -> None]]'
Graphics

$ wo 'Head[GraphPlot[{1 -> 2, 2 -> 3}, EdgeShapeFunction -> "Line"]]'
Graphics

$ wo 'Head[GraphPlot[{1 -> 2, 2 -> 3}, EdgeShapeFunction -> {DirectedEdge[1, 2] -> ({Red, Line[#1]} &)}]]'
Graphics

VertexRenderingFunction -> f draws each vertex with f[{x, y}, name] instead of the built-in disk. The first argument is the vertex's coordinate, the second its name:

$ wo 'Head[GraphPlot[{1 -> 2, 2 -> 3}, VertexRenderingFunction -> (Point[#] &)]]'
Graphics

$ wo 'Head[GraphPlot[{1 -> 2, 2 -> 3}, VertexRenderingFunction -> (Text[#2, #] &)]]'
Graphics

VertexRenderingFunction -> None leaves the vertices undrawn:

$ wo 'Head[GraphPlot[{1 -> 2, 2 -> 3}, VertexRenderingFunction -> None]]'
Graphics