The recent explosion in the availability of genetic sequence data has made large-scale phylogenetic inference routine in many life sciences laboratories. The outcomes of such analyses are, typically, a variety of candidate phylogenetic relationships or tree topologies, even when the power of genome-scale data is exploited. Because much phylogenetic information must be buried in such topology distributions, it is important to reveal that information as effectively as possible; however, existing methods need to adopt complex structures to represent such information. Hence, researchers, in particular those not experts in evolutionary studies, sometimes hesitate to adopt these methods and much phylogenetic information could be overlooked and wasted. In this paper, we propose the centroid wheel tree representation, which is an informative representation of phylogenetic topology distributions, and which can be readily interpreted even by nonexperts. Furthermore, we mathematically prove this to be the most balanced representation of phylogenetic topologies and efficiently solvable in the framework of the traveling salesman problem, for which very sophisticated program packages are available. This theoretically and practically superior representation should aid biologists faced with abundant data. The centroid representation introduced here is fairly general, so it can be applied to other fields that are characterized by high-dimensional solution spaces and large quantities of noisy data. The software is implemented in Java and available via http://cwt.cb.k.u-tokyo.ac.jp/.