  A neutral network is a subgraph of a Hamming graph, and its principal
eigenvalue determines its robustness: the ability of a population evolving on
it to withstand errors. Here we consider the most robust small neutral
networks: the graphs that interpolate pointwise between hypercube graphs of
consecutive dimension (the point, line, line and point in the square, square,
square and point in the cube, and so on). We prove that the principal
eigenvalue of the adjacency matrix of these graphs is bounded by the logarithm
of the number of vertices, and we conjecture an analogous result for Hamming
graphs of alphabet size greater than two.
