  In many biological systems, the network of interactions between the elements
can only be inferred from experimental measurements. In neuroscience,
non-invasive imaging tools are extensively used to derive either structural or
functional brain networks in-vivo. As a result of the inference process, we
obtain a matrix of values corresponding to an unrealistic fully connected and
weighted network. To turn this into a useful sparse network, thresholding is
typically adopted to cancel a percentage of the weakest connections. The
structural properties of the resulting network depend on how much of the
inferred connectivity is eventually retained. However, how to fix this
threshold is still an open issue. We introduce a criterion, the efficiency cost
optimization (ECO), to select a threshold based on the optimization of the
trade-off between the efficiency of a network and its wiring cost. We prove
analytically and we confirm through numerical simulations that the connection
density maximizing this trade-off emphasizes the intrinsic properties of a
given network, while preserving its sparsity. Moreover, this density threshold
can be determined a-priori, since the number of connections to filter only
depends on the network size according to a power-law. We validate this result
on several brain networks, from micro- to macro-scales, obtained with different
imaging modalities. Finally, we test the potential of ECO in discriminating
brain states with respect to alternative filtering methods. ECO advances our
ability to analyze and compare biological networks, inferred from experimental
data, in a fast and principled way.
