In recent years, there has been an increasing interest in the study of large-scale brain activity interaction structure from the perspective of complex networks, based on functional magnetic resonance imaging (fMRI) measurements. To assess the strength of interaction (functional connectivity, FC) between two brain regions, the linear (Pearson) correlation coefficient of the respective time series is most commonly used. Since a potential use of nonlinear FC measures has recently been discussed in this and other fields, the question arises whether particular nonlinear FC measures would be more informative for the graph analysis than linear ones. We present a comparison of network analysis results obtained from the brain connectivity graphs capturing either full (both linear and nonlinear) or only linear connectivity using 24 sessions of human resting-state fMRI. For each session, a matrix of full connectivity between 90 anatomical parcel time series is computed using mutual information. For comparison, connectivity matrices obtained for multivariate linear Gaussian surrogate data that preserve the correlations, but remove any nonlinearity are generated. Binarizing these matrices using multiple thresholds, we generate graphs corresponding to linear and full nonlinear interaction structures. The effect of neglecting nonlinearity is then assessed by comparing the values of a range of graph-theoretical measures evaluated for both types of graphs. Statistical comparisons suggest a potential effect of nonlinearity on the local measures-clustering coefficient and betweenness centrality. Nevertheless, subsequent quantitative comparison shows that the nonlinearity effect is practically negligible when compared to the intersubject variability of the graph measures. Further, on the group-average graph level, the nonlinearity effect is unnoticeable.

Institute of Computer Science AS CR Pod vodárenskou věží 2 18207 Prague 8 Czech Republic

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Boccaletti S., Latora V., Moreno Y., Chavez M., and Hwang D.-U., Phys. Rep. 424, 175 (2006).10.1016/j.physrep.2005.10.009 DOI

Donges J. F., Zou Y., Marwan N., and Kurths J., Eur. Phys. J. Spec. Top. 174,157 (2009).10.1140/epjst/e2009-01098-2 DOI

Bullmore E. and Sporns O., Nat. Rev. Neurosci. 10, 186 (2009).10.1038/nrn2575 PubMed DOI

Kreuz T., Mormann F., Andrzejak R. G., Kraskov A., Lehnertz K., and Grassberger P., Physica D 225, 29 (2007).10.1016/j.physd.2006.09.039 DOI

Lehnertz K., Bialonski S., Horstmann M.-T., Krug D., Rothkegel A., Staniek M., and Wagner T., J. Neurosci. Methods 183, 42 (2009).10.1016/j.jneumeth.2009.05.015 PubMed DOI

Pereda E., Quiroga R. Q., and Bhattacharya J., Prog. Neurobiol. 77, 1 (2005).10.1016/j.pneurobio.2005.10.003 PubMed DOI

Hlavackova-Schindler K., Palus M., Vejmelka M., and Bhattacharya J., Phys. Rep. 441, 1 (2007).10.1016/j.physrep.2006.12.004 DOI

Palus M., Albrecht V., and Dvorak I., Phys. Lett. A 175, 203 (1993).10.1016/0375-9601(93)90827-M DOI

Palus M., Physica D 80, 186 (1995).10.1016/0167-2789(95)90079-9 DOI

Palus M., Phys. Lett. A 213, 138 (1996).10.1016/0375-9601(96)00116-8 DOI

Palus M., Contemp. Phys. 48, 307 (2007).10.1080/00107510801959206 DOI

Theiler J., Eubank S., Longtin A., Galdrikian B., and Farmer J. D., Physica D 58, 77 (1992).10.1016/0167-2789(92)90102-S DOI

Vejmelka M. and Palus M., Phys. Rev. E 77, 026214 (2008).10.1103/PhysRevE.77.026214 PubMed DOI

Palus M. and Novotna D., Phys. Lett. A 193, 67 (1994).10.1016/0375-9601(94)91002-2 DOI

Benitez R., Alvarez-Lacalle E., Echebarria B., Gomis P., Vallverdu M., and Caminal P., Med. Eng. Phys. 31, 660 (2009).10.1016/j.medengphy.2008.12.006 PubMed DOI

Palus M., Biol. Cybern. 75, 389 (1996).10.1007/s004220050304 PubMed DOI

Palus M., Komarek V., Hrncir Z., and Prochazka T., Theory Biosci. 118, 179 (1999).

Alonso J. F., Mananas M. A., Romero S., Hoyer D., Riba J., and Barbanoj M. J., Hum. Brain Mapp. 31, 487 (2010).10.1002/hbm.20881 PubMed DOI PMC

Alonso J. F., Poza J., Mananas M. A., Romero S., Fernandez A., and Hornero R., Ann. Biomed. Eng. 39(1), 524 (2011).10.1007/s10439-010-0155-7 PubMed DOI

Wang J., Zuo X., and He Y., Front. Syst. Neurosci. 4, 16 (2010).10.3389/fnsys.2010.00016 PubMed DOI PMC

Hlinka J., Palus M., Vejmelka M., Mantini D., and Corbetta M., Neuroimage 54, 2218 (2011).10.1016/j.neuroimage.2010.08.042 PubMed DOI PMC

Ogawa S., Lee T. M., Kay A. R., and Tank D. W., Proc. Natl. Acad. Sci. U.S.A. 87, 9868 (1990).10.1073/pnas.87.24.9868 PubMed DOI PMC

Statistical Parametric Mapping: The Analysis of Functional Brain Images, edited by Friston K. J., Ashburner J., Kiebel S. J., Nichols T. E., and Penny W. D. (Academic, London, 2007).

Tzourio-Mazoyer N., Landeau B., Papathanassiou D., Crivello F., Etard O., Delcroix N., Mazoyer B., and Joliot M., Neuroimage 15, 273 (2002).10.1006/nimg.2001.0978 PubMed DOI

Prichard D. and Theiler J., Phys. Rev. Lett. 73, 951 (1994).10.1103/PhysRevLett.73.951 PubMed DOI

Palus M., Phys. Lett. A 235, 341 (1997).10.1016/S0375-9601(97)00635-X DOI

Schreiber T. and Schmitz A., Phys. Rev. Lett. 77, 635 (1996).10.1103/PhysRevLett.77.635 PubMed DOI

Palus M., Neural Network World 7, 269 (1997).

Palus M. and Vejmelka M., Phys. Rev. E 75, 056211 (2007).10.1103/PhysRevE.75.056211 PubMed DOI

Bollobas B., Modern Graph Theory (Springer, New York, 1998).

Diestel R., Graph Theory (Springer, New York, 2000).

Godsil C. and Royle G., Algebraic Graph Theory (Springer, New York, 2001).

Networks, Topology and Dynamics: Theory and Applications to Economics and Social Systems, edited by Torriero A.Naimzada A. K., and Stefani S. (Springer, New York, 2008).

Schultz H. P., J. Chem. Inf. Comput. Sci. 29, 227 (1989).10.1021/ci00063a012 DOI

Papin J. A., Price N. D., Wiback S. J., Fell D. A., and Palsson B. O., Trends Biochem. Sci. 28, 250 (2003).10.1016/S0968-0004(03)00064-1 PubMed DOI

Barabasi A. L. and Albert R., Science 286, 509 (1999).10.1126/science.286.5439.509 PubMed DOI

Watts D. J. and Strogatz S. H., Nature (London) 393, 440 (2009).10.1038/30918 PubMed DOI

Freeman L. C., Soc. Networks 1, 215 (1978–1979).10.1016/0378-8733(78)90021-7 DOI

Brandes U., J. Math. Sociol. 25, 163 (2001).10.1080/0022250X.2001.9990249 DOI

Brandes U., Soc. Networks 30, 136 (2008).10.1016/j.socnet.2007.11.001 DOI

Holme P. and Kim B. J., Phys. Rev. E 65, 066109 (2002).10.1103/PhysRevE.65.066109 PubMed DOI

Latora V. and Marchiori M., Phys. Rev. Lett. 87, 198701 (2001).10.1103/PhysRevLett.87.198701 PubMed DOI

Latora V. and Marchiori M., Eur. Phys. J. B 32, 249 (2003).10.1140/epjb/e2003-00095-5 DOI

Newman M. E. J., Phys. Rev. Lett. 89, 208701 (2002).10.1103/PhysRevLett.89.208701 PubMed DOI

Gallos L. K., Song C., and Makse H. A., Phys. Rev. Lett. 100, 248701 (2008).10.1103/PhysRevLett.100.248701 PubMed DOI

Newman M. E. J., Phys. Rev. E 67, 026126 (2003).10.1103/PhysRevE.67.026126 PubMed DOI

Newman M. E. J., Strogatz S. H., and Watts D. J., Phys. Rev. E 64, 026118 (2001).10.1103/PhysRevE.64.026118 PubMed DOI

Concrete and Abstract Voronoi Diagrams (Lecture Notes in Computer Science), edited by Klein R. (Springer, New York, 1990).

Timmer J., Phys. Rev. E 58, 5153 (1998).10.1103/PhysRevE.58.5153 DOI

Witt A., Kurths J., and Pikovsky A., Phys. Rev. E 58, 1800 (1998).10.1103/PhysRevE.58.1800 DOI

Rieke C., Mormann F., Andrzejak R. G., Kreuz T., David P., Elger C. E., and Lehnertz K., IEEE Trans. Biomed. Eng. 50, 634 (2003).10.1109/TBME.2003.810684 PubMed DOI

Faes L., Zhao H., Chon K. H., and Nollo G., IEEE Trans. Biomed. Eng. 56, 685 (2009).10.1109/TBME.2008.2009358 PubMed DOI

Bandt C. and Pompe B., Phys. Rev. Lett. 88, 174102 (2002).10.1103/PhysRevLett.88.174102 PubMed DOI

Northoff G., Qin P., and Nakao T., Trends Neurosci. 33, 277 (2010).10.1016/j.tins.2010.02.006 PubMed DOI

Smith S. M., Fox P. T., Miller K. L., Glahn D. C., Fox P. M., Mackay C. E., Filippini N., Watkins K. E., Toro R., Laird A. R., and Beckmann C. F., Proc. Natl. Acad. Sci. U.S.A. 106, 13040 (2009).10.1073/pnas.0905267106 PubMed DOI PMC

Broyd S. J., Demanuele C., Debener S., Helps S. K., James C. J., and Sonuga-Barke E. J. S., Neurosci. Biobehav. Rev. 33, 279 (2009).10.1016/j.neubiorev.2008.09.002 PubMed DOI

Fornito A. and Bullmore E. T., Curr. Opin. Psychiatr. 23, 239 (2010).10.1097/YCO.0b013e328337d78d PubMed DOI

Stephan K. E., Kasper L., Harrison L. M., Daunizeau J., den Ouden H. E. M., Breakspear M., and Friston K. J., Neuroimage 42, 649 (2008).10.1016/j.neuroimage.2008.04.262 PubMed DOI PMC

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