  Most agent-based models include a social network that describes the structure
of interactions within the artificial population. Because of the dramatic
impact of this structure on the simulated dynamics, modelers create this
network for it to match criteria of plausibility (e.g. the small-world
property). Networks are actually created by one network generator compliant
with these criteria, like the Watts-Strogatz algorithm in the case of
small-world networks. However, this practice comes to study the model's
dynamics over the specific networks generated by one algorithm instead of the
dynamics over the class of networks of interest, possibly inducing a strong
bias in results. We identify three problematics related to this bias: (i)
representativity of a network generator to a class of networks, (ii)
conclusiveness of simulations over a class of networks and (iii) the gain in
conclusiveness when refining the criteria for network choice. We propose an
experimental protocol and instantiate it on small-world networks for epidemics,
opinion and culture dynamics. We show that (i) Watts-Strogatz networks are not
representative of small-world networks (ii) simulation results over
small-worlds are arguably inconclusive, and (iii) even small-world networks
having the same size, density, transitivity and average path length do not lead
to coherent results. Beyond questioning the relevance of simulation results
obtained from artificial networks, this research also constitute one more
argument for the exploration of other approaches that are not solely focused on
networks' statistical properties.
