# A Class of Representations for Evolving Graphs

### Daniel Ashlock, Lee-Ann Barlow, and Justin Schonfeld

Submitted to CEC 2105

This study introduces a parametrized family of representations for
evolving graphs together with a benchmark function that is
diagnostic of an important quality of a representation for graph
evolution, its natural distribution of edge densities. The new
benchmark function, the edge maximization function, is equivalent to
the trivial onemax function for some representations and represents a
difficult problem for others. The utility of the edge maximization
function lies in the fact that the edge density distribution in a
graph is a critical parameter for evolving graphs and so performance
of a representation on edgemax is diagnostic of an important aspect of
its behavior. Three cases of the edgemax problem are examined using
six different parameterizations of the new representation. The
representations presented here are generative and so need not have any
particular length. For each problem case and parametrization of the
representation two lengths of chromosome are examined, one that is
just long enough to solve the benchmark problem and one that is 10%
longer. The edgemax is found to be diagnostic of representation
properties.