Communities in C.elegans connectome through the prism of non-backtracking walks
arXiv:2207.11282 · doi:10.1038/s41598-023-49503-5
Abstract
The fundamental relationship between the mesoscopic structure of neuronal circuits and organismic functions they subserve is one of the major challenges in contemporary neuroscience. Formation of structurally connected modules of neurons enacts the conversion from single-cell firing to large-scale behaviour of an organism, highlighting the importance of their accurate profiling in the data. While connectomes are typically characterized by significant sparsity of neuronal connections, recent advances in network theory and machine learning have revealed fundamental limitations of traditionally used community detection approaches in cases where the network is sparse. Here we studied the optimal community structure in the structural connectome of C.elegans, for which we exploited a non-conventional approach that is based on non-backtracking random walks, virtually eliminating the sparsity issue. In full agreement with the previous asymptotic results, we demonstrated that non-backtracking walks resolve the ground truth annotation into clusters on stochastic block models (SBM) with the size and density of the connectome better than the spectral methods related to simple random walks. Based on the cluster detectability threshold, we determined that the optimal number of modules in a recently mapped connectome of C.elegans is 10, which precisely corresponds to the number of isolated eigenvalues in the spectrum of the non-backtracking flow matrix. Broadly, our work provides a robust network-based framework to reveal mesoscopic structures in sparse connectomic datasets, paving way to further investigation of connectome mechanisms for different functions.
arXiv commentThis work previously appeared as arXiv:2207.00767 under an accidental replacement
References in corpus (19)
- Finding and evaluating community structure in networks
- Modularity and community structure in networks
- Finding community structure in networks using the eigenvectors of matrices
- The diameter of the world wide web
- Hierarchical organization of modularity in metabolic networks
- Statistical Mechanics of Community Detection
- How Popular is Your Paper? An Empirical Study of the Citation Distribution
- Structural Properties of the Caenorhabditis elegans Neuronal Network
- The map equation
- Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications
- Spectral redemption: clustering sparse networks
- Extracting the hierarchical organization of complex systems
- Analysis of the structure of complex networks at different resolution levels
- Phase transition in the detection of modules in sparse networks
- Graph spectra and the detectability of community structure in networks
- Percolation on sparse networks
- Multiway spectral community detection in networks
- Mesoscopic organization reveals the constraints governing C. elegans nervous system
- Finding communities in sparse networks