The susceptible, infected, removed model for epidemics assumes that the population in which the epidemic takes place is well mixed. This strong assumption can be relaxed by permitting the epidemic to spread only along the links of a contact network or graph. This study uses evolutionary computation to search for graphs that exhibit one of two extreme behaviors: maximum epidemic duration or maximal number of individuals catching the disease. The focus of the paper is on comparison of two representations for evolvable networks. The first makes local expansions of the network specified by a linear chromosome. The second, a permutation-based representation, joins a large cycle with another cycle specified by the permutation. The linear chromosome representation, based on iterated simplexification, yields inferior results in both fitness measures but creates networks with a structure more like a personal contact network. Location of such behaviorally extreme networks will provide a set of test cases for intervention strategies as well as providing conjectures to focus standard mathematical investigation of the types of networks that yield extreme behavior. This study also proposes a testing protocol for network representations for epidemic modeling.