  The Moran process on graphs is a popular model to study the dynamics of
evolution in a spatially structured population. Exact analytical solutions for
the fixation probability and time of a new mutant have been found for only a
few classes of graphs so far. Simulations are time-expensive and many
realizations are necessary, as the variance of the fixation times is high. We
present an algorithm that numerically computes these quantities for arbitrary
small graphs by an approach based on the transition matrix. The advantage over
simulations is that the calculation has to be executed only once. Building the
transition matrix is automated by our algorithm. This enables a fast and
interactive study of different graph structures and their effect on fixation
probability and time. We provide a fast implementation in C with this note
https://github.com/hindersin/efficientFixation. Our code is very flexible, as
it can handle two different update mechanisms (Birth-death or death-Birth), as
well as arbitrary directed or undirected graphs.
