I'd like to draw something like the following graph:

testGraph = Graph[{1 \[UndirectedEdge] 2, 1 \[UndirectedEdge] 4, 2 \[UndirectedEdge] 3, 2 \[UndirectedEdge] 5, 3 \[UndirectedEdge] 4}, VertexLabels -> {1 -> "1", 2 -> "2", 3 -> "3", 4 -> "4", 5 -> "5"}, VertexCoordinates -> {{0, 0}, {1, 1}, {2, 3}, {4, 1}, {3, 3}}, ImagePadding -> 10] 

However, without changing any of the explicitly specified vertex positions, I'd like edges to curve to avoid vertices. For example, while it's fine that the edges between vertices 1 and 5, 2 and 5, and 3 and 4 cross, it's no good that the edge between vertices 1 and 5 passes through a small sphere around vertex 2.

Is there any way to avoid this in Mathematica v9? This is a dream, however, could I specify a length for an edge and have it travel along an arc to meet that length requirement provided stationary vertices?

A hack would involve creating a set of edges between "invisible" vertices, however, it would take a lot of invisible vertices to create an appropriate curvature effect, and this doesn't seem like the right thing to do.

I'd like to draw something like the following graph:

testGraph = Graph[{1 \[UndirectedEdge] 2, 1 \[UndirectedEdge] 4, 2 \[UndirectedEdge] 3, 2 \[UndirectedEdge] 5, 3 \[UndirectedEdge] 4}, VertexLabels -> {1 -> "1", 2 -> "2", 3 -> "3", 4 -> "4", 5 -> "5"}, VertexCoordinates -> {{0, 0}, {1, 1}, {2, 3}, {4, 1}, {3, 3}}, ImagePadding -> 10] 

However, without changing any of the explicitly specified vertex positions, I'd like edges to curve to avoid vertices. For example, while it's fine that the edges between vertices 2 and 5, and 3 and 4 cross, what if I have an edge between vertices 1 & 5 (if I actually do this, Mathematica v9 appears to no longer respect my vertex coordinates) and what if I would like this edge not to pass through a small sphere about vertex 2?

Is there any way to enforce vertex positionings while allowing for curved edges that avoid vertices in Mathematica v9? This is a dream, however, could I specify a length for an edge and have it travel along an arc to meet that length requirement provided stationary vertices?

A hack would involve creating a set of edges between "invisible" vertices, however, it would take a lot of invisible vertices to create an appropriate curvature effect, and this doesn't seem like the right thing to do.

I'd like to draw something like the following graph:

testGraph = Graph[{1 \[UndirectedEdge] 2, 1 \[UndirectedEdge] 4, 2 \[UndirectedEdge] 3, 2 \[UndirectedEdge] 5, 3 \[UndirectedEdge] 4}, VertexLabels -> {1 -> "1", 2 -> "2", 3 -> "3", 4 -> "4", 5 -> "5"}, VertexCoordinates -> {{0, 0}, {1, 1}, {2, 3}, {4, 1}, {3, 3}}, ImagePadding -> 10] 

However, without changing any of the explicitly specified vertex positions, I'd like edges to curve to avoid vertices. For example, while it's fine that the edges between vertices 1 and 5, 2 and 5, and 3 and 4 cross, it's no good that the edge between vertices 1 and 5 passes through a small sphere around vertex 2.

Is there any way to avoid this in Mathematica v9? This is a dream, however, could I specify a length for an edge and have it travel along an arc to meet that length requirement provided stationary vertices?

A hack would involve creating a set of edges between "invisible" vertices, however, it would take a lot of invisible vertices to create an appropriate curvature effect, and this doesn't seem like the right thing to do.

I'd like to draw something like the following graph:

testGraph = Graph[{1 \[UndirectedEdge] 2, 1 \[UndirectedEdge] 4,  2 \[UndirectedEdge] 3, 2 \[UndirectedEdge] 5,  3 \[UndirectedEdge] 4},  VertexLabels -> {1 -> "1", 2 -> "2", 3 -> "3", 4 -> "4", 5 -> "5"},  VertexCoordinates -> {{0, 0}, {1, 1}, {2, 3}, {4, 1}, {3, 3}},  ImagePadding -> 10] 

However, without changing any of the explicitly specified vertex positions, I'd like edges to curve to avoid vertices. For example, while it's fine that the edges between vertices 1 and 5, 2 and 5, and 3 and 4 cross, it's no good that the edge between vertices 1 and 5 passes through a small sphere around vertex 2.

Is there any way to avoid this in Mathematica v9? This is a dream, however, could I specify a length for an edge and have it travel along an arc to meet that length requirement provided stationary vertices?

A hack would involve creating a set of edges between "invisible" vertices, however, it would take a lot of invisible vertices to create an appropriate curvature effect, and this doesn't seem like the right thing to do.