Partitioning directed graphs based on modularity and information flow

Although models of the behavior of individual neurons and synapses are now well established, understanding the way in which they cooperate in large ensembles remains a major scientific challenge. We present two novel graph theory methods to study cortical interactions and image the highly organized structure of large scale networks. First, we present a new method to partition directed graphs into modules, based on modularity and an expected network conditioned on the in- and out-degrees of all nodes. We also propose a method to segment graphs based on information flow. These methods are combined to study the community structure of brain networks and information flow within the modules.

[1]  Bruce A. Reed,et al.  A Critical Point for Random Graphs with a Given Degree Sequence , 1995, Random Struct. Algorithms.

[2]  M E J Newman,et al.  Finding and evaluating community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  M E J Newman,et al.  Modularity and community structure in networks. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[4]  V. Swarnkar,et al.  Left-Right Information flow in the Brain during EEG arousals , 2006, 2006 International Conference of the IEEE Engineering in Medicine and Biology Society.

[5]  P. Rossini,et al.  Directional information flows between brain hemispheres during presleep wake and early sleep stages. , 2007, Cerebral cortex.

[6]  Sergio Gómez,et al.  Size reduction of complex networks preserving modularity , 2007, ArXiv.

[7]  M. P. van den Heuvel,et al.  Normalized Cut Group Clustering of Resting-State fMRI Data , 2008, PloS one.

[8]  O. Sporns,et al.  Mapping the Structural Core of Human Cerebral Cortex , 2008, PLoS biology.

[9]  E A Leicht,et al.  Community structure in directed networks. , 2007, Physical review letters.

[10]  Richard M. Leahy,et al.  Identifying true cortical interactions in MEG using the nulling beamformer , 2010, NeuroImage.

[11]  Edward T. Bullmore,et al.  Frontiers in Systems Neuroscience Systems Neuroscience , 2022 .

[12]  Richard M. Leahy,et al.  Statistically optimal graph partition method based on modularity , 2010, 2010 IEEE International Symposium on Biomedical Imaging: From Nano to Macro.

[13]  S.,et al.  An Efficient Heuristic Procedure for Partitioning Graphs , 2022 .