Relative Strength Variability Measures for Brain Structural Connectomes and Their Relationship With Cognitive Functioning

In this work, we propose a new class of graph measures for weighted connectivity information in the human brain based on node relative strengths: relative strength variability (RSV), measuring susceptibility to targeted attacks, and hierarchical RSV (hRSV), a first weighted statistical complexity measure for networks. Using six different network weights for structural connectomes from the UK Biobank, we conduct comprehensive analyses to explore relationships between the RSV and hRSV, and (i) other known network measures, (ii) general cognitive function (' <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>g</mml:mi></mml:mrow> <mml:annotation>$$ g $$</mml:annotation></mml:semantics> </mml:math> '). Both measures exhibit low correlations with other graph measures across all connectivity weightings indicating that they capture new information of the brain connectome. We found higher <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>g</mml:mi></mml:mrow> <mml:annotation>$$ g $$</mml:annotation></mml:semantics> </mml:math> was associated with lower RSV and lower hRSV. That is, higher <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>g</mml:mi></mml:mrow> <mml:annotation>$$ g $$</mml:annotation></mml:semantics> </mml:math> was associated with higher resistance to targeted attack and lower statistical complexity. Moreover, the proposed measures had consistently stronger associations with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>g</mml:mi></mml:mrow> <mml:annotation>$$ g $$</mml:annotation></mml:semantics> </mml:math> than other widely used graph measures including clustering coefficient and global efficiency and were incrementally significant for predicting <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>g</mml:mi></mml:mrow> <mml:annotation>$$ g $$</mml:annotation></mml:semantics> </mml:math> above other measures for five of the six network weights. Overall, we present a new class of weighted network measures based on variations of relative node strengths which significantly improved prediction of general cognition from traditional weighted structural connectomes.