# Why would the color of graph change once the number of vertexes reach 1000?

I have created 3 graphs for vertexes number 998, 999 and 1000 as below:-

f[m_] := Graph[Range@MeshCellCount[m, 0], MeshCells[m, 1][[All, 1]], EdgeWeight -> PropertyValue[{m, 1}, MeshCellMeasure], VertexCoordinates -> MeshCoordinates[m]];
BlockRandom[SeedRandom[12]; pts998 = RandomReal[100, {998, 3}];]
BlockRandom[SeedRandom[12]; pts999 = RandomReal[100, {999, 3}];]
BlockRandom[SeedRandom[12]; pts1000 = RandomReal[100, {1000, 3}];]
f@DelaunayMesh[pts998]
f@DelaunayMesh[pts999]
f@DelaunayMesh[pts1000]


I noted that the color of 998 and 999 are same, but that of 1000 is different. Why would that happen and how to avoid the change? Many thanks!

998:-

999:-

1000:-

It's for performance reasons. If there are too many edges, then it is too costly to render all of them as tubes. Moreover, tubes have a certain thickness, so they also don't help to distinguish edges. This might be another reason.

The threshold appears to be 1000 vertices. With less than 1000 vertices, Graph uses PlotTheme -> "Default" as plot theme. With 1000 or more vertices, as Szabolcs said in the comments, Graph uses PlotTheme -> "LargeNetworkDefault" for graphs with 1000 vertices or more.

You can still enforce the rendering with default plot style if you use

f[m_] := Graph[Range@MeshCellCount[m, 0], MeshCells[m, 1][[All, 1]],
EdgeWeight -> PropertyValue[{m, 1}, MeshCellMeasure],
VertexCoordinates -> MeshCoordinates[m],
PlotTheme -> "Default"
];

• It's LargeNetworkDefault. Can you edit this into the answer to make it easier to search for? – Szabolcs Jun 18 '18 at 6:44
• @Szabolcs Ah, great! I added it. Thank you for the hint! – Henrik Schumacher Jun 18 '18 at 6:48