Complex networks have been observed to comprise small-world properties, believed to represent an optimal organization of local specialization and global integration of information processing at reduced wiring cost. Here, we applied magnitude squared coherence to resting magnetoencephalographic time series in reconstructed source space, acquired from controls and patients with schizophrenia, and generated frequency-dependent adjacency matrices modeling functional connectivity between virtual channels. After configuring undirected binary and weighted graphs, we found that all human networks demonstrated highly localized clustering and short characteristic path lengths. The most conservatively thresholded networks showed efficient wiring, with topographical distance between connected vertices amounting to one-third as observed in surrogate randomized topologies. Nodal degrees of the human networks conformed to a heavy-tailed exponentially truncated power-law, compatible with the existence of hubs, which included theta and alpha bilateral cerebellar tonsil, beta and gamma bilateral posterior cingulate, and bilateral thalamus across all frequencies. We conclude that all networks showed small-worldness, minimal physical connection distance, and skewed degree distributions characteristic of physically-embedded networks, and that these calculations derived from graph theoretical mathematics did not quantifiably distinguish between subject populations, independent of bandwidth. However, post-hoc measurements of edge computations at the scale of the individual vertex revealed trends of reduced gamma connectivity across the posterior medial parietal cortex in patients, an observation consistent with our prior resting activation study that found significant reduction of synthetic aperture magnetometry gamma power across similar regions. The basis of these small differences remains unclear.
Keywords: schizophrenia, small world, magnitude squared coherence, clustering coefficient, path length, exponentially truncated power-law, synthetic aperture magnetometry, default network
Citation: Rutter L, Nadar SR, Holroyd T, Carver FW, Apud J, Weinberger DR and Coppola R (2013) Graph theoretical analysis of resting magnetoencephalographic functional connectivity networks. Front. Comput. Neurosci. 7:93. doi: 10.3389/fncom.2013.00093
Received: 04 January 2013; Accepted: 21 June 2013;
Published online: 12 July 2013.
Edited by:Hava T. Siegelmann, Rutgers University, USA
Reviewed by:Abdelmalik Moujahid, University of the Basque Country UPV/EHU, Spain
Copyright © 2013 Rutter, Nadar, Holroyd, Carver, Apud, Weinberger and Coppola. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in other forums, provided the original authors and source are credited and subject to any copyright notices concerning any third-party graphics etc.
*Correspondence: Richard Coppola, National Institute of Mental Health, Building 10-Room 3C119, 10 Center Drive, Bethesda, MD 20892, USA e-mail: firstname.lastname@example.org