A topological criterion for filtering information in complex brain networks

TL;DR

This paper introduces a new topological criterion called ECO for selecting thresholds in brain network analysis, optimizing the trade-off between network efficiency and wiring cost to improve the interpretability of inferred biological networks.

Contribution

The paper proposes the ECO criterion for thresholding brain networks, providing an analytical and numerical validation that emphasizes intrinsic network properties while maintaining sparsity.

Findings

ECO effectively identifies meaningful network thresholds across different brain scales.

The optimal connection density follows a power-law based on network size.

ECO improves discrimination of brain states compared to other filtering methods.

Abstract

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.