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]