  We apply an information theoretic treatment of action potential time series
measured with microelectrode arrays to estimate the connectivity of mammalian
neuronal cell assemblies grown {\it in vitro}. We infer connectivity between
two neurons via the measurement of the mutual information between their spike
trains. In addition we measure higher point multi-informations between any two
spike trains conditional on the activity of a third cell, as a means to
identify and distinguish classes of functional connectivity among three
neurons. The use of a conditional three-cell measure removes some
interpretational shortcomings of the pairwise mutual information and sheds
light into the functional connectivity arrangements of any three cells. We
analyze the resultant connectivity graphs in light of other complex networks
and demonstrate that, despite their {\it ex vivo} development, the connectivity
maps derived from cultured neural assemblies are similar to other biological
networks and display nontrivial structure in clustering coefficient, network
diameter and assortative mixing. Specifically we show that these networks are
weakly disassortative small world graphs, which differ significantly in their
structure from randomized graphs with the same degree. We expect our analysis
to be useful in identifying the computational motifs of a wide variety of
complex networks, derived from time series data.
