The unit distance graph on the three-dimensional integer lattice has a vertex for each lattice point; each vertex has exactly six neighbors. It is possible to remove some of the points from the lattice, so that each remaining point has exactly three remaining neighbors, and so that the induced subgraph of these points has no cycles shorter than ten edges. There are four ways to do this, one of which is isomorphic as an abstract graph to the Laves graph. However, its vertices are in different positions than the more-symmetric, conventional geometric construction.
Another subgraph of the simple cubic net isomorphic to the Laves graph is obtained by removing half of the edges in a certain way. The resulting structure, called semi-simple cubic lattice, also has lower symmetry than the Laves graph itself.