Origin of Hyperbolicity in Brain-to-Brain Coordination Networks

Abstract

Hyperbolicity or negative curvature of complex networks is the intrinsic geometric proximity of nodes in the graph metric space, which implies an improved network function. Here, we investigate hidden combinatorial geometries in brain-to-brain coordination networks arising through social communications. The networks originate from correlations among EEG signals previously recorded during spoken communications comprising of 14 individuals with 24 speaker-listener pairs. We find that the corresponding networks are δ-hyperbolic with δ max = 1 and the graph diameter D = 3 in each brain. While the emergent hyperbolicity in the two-brain networks varies satisfying δ max /D/2 ≤ 1 and can be attributed to the topology of the subgraph formed around the cross-brains linking channels. We identify these subgraphs in each studied two-brain network and decompose their structure into simple geometric descriptors (triangles, tetrahedra and cliques of higher orders) that contribute to hyperbolicity. Considering topologies that exceed two separate brain networks as a measure of coordination synergy between the brains, we identify different neural correlation patterns ranging from weak coordination to super-brain structure. These topology features are in qualitative agreement with the listener's self-reported ratings of own experience and quality of the speaker, suggesting that studies of the cross-brain connector networks can reveal new insight into the neural mechanisms underlying human social behavior.

Functional Geometry of Human Connectomes

“…Based on the brain imaging data, the methodology developed in this work would be suitable to reveal subtle differences between pairs of brains as well as changes in the brain of the same individual. Similar studies have been done with the patterns induced by the brain spontaneous fluctuations and content-related activity recorded by EEG 27,30,71 , complementing the traditional methods. The application of our methodology to these issues warants a separate study which would include a more detailed investigation of the role of orientation and the weights of the edges.…”

“…In this sense, the complete graph and associated tree are ideally hyperbolic, characterised by the hyperbolicity parameter . The graphs with small values of δ are subject to intensive investigations for their ubiquity in natural and social systems, as well as in technology applications 24,25,30,33,48 . Moreover, current theoretical studies reveal that Gromov hyperbolic graphs with a small hyperbolicity parameter have specific mathematical properties 48 .…”

Homological scaffold via minimal homology bases

“…The possible applications in which the minimal scaffold could provide novel insight into the structure of brain data are many: any relatively small correlation matrix could be either compressed or its patterns analyzed, as is often the case in EEG 42 , 44 , 79 , 80 or neuronal 38 studies, and in fMRI ones when using rather coarse atlases (e.g. 81 , 82 ).…”

The inherent community structure of hyperbolic networks

“…In parallel with the success of hyperbolic models, there have also been several studies carried out focusing on possible hidden metric spaces behind real networks, starting with the examination of the self-similarity of scale-free networks [19], followed by reports on the hyperbolicity of protein interaction networks [23,24], the Internet [25][26][27][28][29], brain networks [30,31], or the world trade network [32]. Furthermore, a connection between the navigability of networks and hyperbolic spaces was shown [25,33], the geometric nature of weights [34] and clustering [35,36] was demonstrated, methods for measuring the hyperbolicity of networks were introduced [37,38], and practical fast algorithms for generating hyperbolic networks were proposed [21].…”