  Network graphs have become a popular tool to represent complex systems
composed of many interacting subunits; especially in neuroscience, network
graphs are increasingly used to represent and analyze functional interactions
between neural sources. Interactions are often reconstructed using pairwise
bivariate analyses, overlooking their multivariate nature: it is neglected that
investigating the effect of one source on a target necessitates to take all
other sources as potential nuisance variables into account; also combinations
of sources may act jointly on a given target. Bivariate analyses produce
networks that may contain spurious interactions, which reduce the
interpretability of the network and its graph metrics. A truly multivariate
reconstruction, however, is computationally intractable due to combinatorial
explosion in the number of potential interactions. Thus, we have to resort to
approximative methods to handle the intractability of multivariate interaction
reconstruction, and thereby enable the use of networks in neuroscience. Here,
we suggest such an approximative approach in the form of an algorithm that
extends fast bivariate interaction reconstruction by identifying potentially
spurious interactions post-hoc: the algorithm flags potentially spurious edges,
which may then be pruned from the network. This produces a statistically
conservative network approximation that is guaranteed to contain non-spurious
interactions only. We describe the algorithm and present a reference
implementation to test its performance. We discuss the algorithm in relation to
other approximative multivariate methods and highlight suitable application
scenarios. Our approach is a tractable and data-efficient way of reconstructing
approximative networks of multivariate interactions. It is preferable if
available data are limited or if fully multivariate approaches are
computationally infeasible.
