Network alignment and similarity reveal atlas-based topological differences in structural connectomes

Author Summary An important part of our current understanding of the structure of the human brain relies on the concept of brain network, which is obtained by looking at how different brain regions are connected with each other. In this paper we present a strategy for choosing a suitable parcellation of the brain for structural connectivity studies by making use of the concepts of network alignment and similarity. To do so, we design a novel similarity measure between weighted networks called graph Jaccard index, and a new network alignment technique called WL-align. By assessing the possibility to retrieve graph matchings that provide highly similar graphs, we show that morphology- and structure-based atlases define brain networks that are more topologically robust across a wide range of resolutions. The interactions between different brain regions can be modeled as a graph, called connectome, whose nodes correspond to parcels from a predefined brain atlas. The edges of the graph encode the strength of the axonal connectivity between regions of the atlas that can be estimated via diffusion magnetic resonance imaging (MRI) tractography. Herein, we aim to provide a novel perspective on the problem of choosing a suitable atlas for structural connectivity studies by assessing how robustly an atlas captures the network topology across different subjects in a homogeneous cohort. We measure this robustness by assessing the alignability of the connectomes, namely the possibility to retrieve graph matchings that provide highly similar graphs. We introduce two novel concepts. First, the graph Jaccard index (GJI), a graph similarity measure based on the well-established Jaccard index between sets; the GJI exhibits natural mathematical properties that are not satisfied by previous approaches. Second, we devise WL-align, a new technique for aligning connectomes obtained by adapting the Weisfeiler-Leman (WL) graph-isomorphism test. We validated the GJI and WL-align on data from the Human Connectome Project database, inferring a strategy for choosing a suitable parcellation for structural connectivity studies. Code and data are publicly available.