Structural networks of human brain: spectral analysis

Bobyleva A.V., Pospelov N.A.1, Nechaev S.K.2, Gorsky A.S.3, Valba O.V.4

Московский государственный университет им. М.В. Ломоносова, Биологический ф-т, каф. биофизики, Россия, 119991, г. Москва, Ленинские горы, 1 стр 12, Тел. 8(977)131-98-05, E-mail:

1Институт перспективных исследований мозга МГУ, Россия, 119192, г. Москва, Ломоносовский пр., 27, корпус 1, Тел. 8(495)938-25-48, E-mail:

2Universite Paris-Saclay, France, 91190, Orsay, Bâtiment Bréguet, 3 Rue Joliot Curie 2e ét, E-mail:

3Институт проблем передачи информации имени А. А. Харкевича РАН, Россия, 127051, г. Москва, Большой Каретный пер., д.19 стр. 1, Тел. 8(495)650-42-25, E-mail:

4Национальный исследовательский университет «Высшая школа экономики», Россия, 123592, г. Москва, ул. Таллинская, 34, E-mail:

The brain is a complex network of structurally and functionally interconnected elements - a connectome. Studying the structure of this network as a whole is important for understanding the principles of information processing in the brain and the connection between its structural and functional architecture.

Brain networks can be represented mathematically as a graph G = (V, E), where V is a set of nodes representing groups of neurons or brain regions, E are edges connecting them through nerve fibers. In this work, we analyzed experimentally obtained connectomes using diffusion MRI, presented in the form of graphs taken from the Human Connectome Project database. Connectome analysis was performed in the Python programming language.

The results of the analysis show that brain networks have a number of unique spectral properties: 1) pronounced dynamics of λ3 and λ4 - the eigenvalues of the Laplacian of the graph (characterizing the degree of connectivity within the hemispheres) when interhemispheric edges are removed; 2) the shape of the spectra of adjacency matrices, which is unusual for random networks; 3) abnormally high overlap of sets of neighbors of nodes; 4) distribution of degrees of nodes with a heavy tail, indicating the presence of hubs in the network - nodes with an abnormally large number of connections.

Based on the results of the analysis of the spectral properties of brain networks, a model was built based on two structural principles (the principle of preferential attachment and metabolic restrictions on the length of connections), reproducing the basic properties of real connectomes. The results obtained are in good agreement with the theory of the influence of geometric constraints on brain function [1] and the principle of hierarchical organization of the connectome.

[1] Pang, J.C., Aquino, K.M., Oldehinkel, M. et al. Geometric constraints on human brain function // Nature V. 618, 2023. P. 566–574.

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