Functional Brain Networks: beyond the small-world paradigm*

Abstract This contribution reviews the current state of the art comprising the application of Complex Networks Theory to the analysis of functional brain networks. We briefly overview the main advances in this field during the last decade and we explain how graph analysis has increased our knowledge about how the brain behaves when performing a specific task or how it fails when a certain pathology arises. We also show the limitations of this kind of analysis, which have been a source of confusion and misunderstanding when interpreting the results obtained. Finally, we discuss possible future directions for the years to come.

[1]  Alan C. Evans,et al.  Small-world anatomical networks in the human brain revealed by cortical thickness from MRI. , 2007, Cerebral cortex.

[2]  G. Sandini,et al.  Graph theoretical analysis of magnetoencephalographic functional connectivity in Alzheimer's disease. , 2009, Brain : a journal of neurology.

[3]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[4]  D. Simard,et al.  Fastest learning in small-world neural networks , 2004, physics/0402076.

[5]  C. Stam,et al.  Small-world networks and epilepsy: Graph theoretical analysis of intracerebrally recorded mesial temporal lobe seizures , 2007, Clinical Neurophysiology.

[6]  O. Sporns,et al.  Motifs in Brain Networks , 2004, PLoS biology.

[7]  M P Young,et al.  Anatomical connectivity defines the organization of clusters of cortical areas in the macaque monkey and the cat. , 2000, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[8]  Lucas Antiqueira,et al.  Analyzing and modeling real-world phenomena with complex networks: a survey of applications , 2007, 0711.3199.

[9]  H. Kowarzyk.  Structure and Function. , 1910, Nature.

[10]  Rodrigo Quian Quiroga,et al.  Nonlinear multivariate analysis of neurophysiological signals , 2005, Progress in Neurobiology.

[11]  E. Bullmore,et al.  Hierarchical Organization of Human Cortical Networks in Health and Schizophrenia , 2008, The Journal of Neuroscience.

[12]  O. Sporns,et al.  Identification and Classification of Hubs in Brain Networks , 2007, PloS one.

[13]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[14]  P. Thiran,et al.  Mapping Human Whole-Brain Structural Networks with Diffusion MRI , 2007, PloS one.

[15]  E. Bullmore,et al.  A Resilient, Low-Frequency, Small-World Human Brain Functional Network with Highly Connected Association Cortical Hubs , 2006, The Journal of Neuroscience.

[16]  P A Robinson,et al.  Geometric effects on complex network structure in the cortex. , 2011, Physical review letters.

[17]  J. A. Almendral,et al.  Reorganization of Functional Networks in Mild Cognitive Impairment , 2011, PloS one.

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

[19]  O. Sporns,et al.  Complex brain networks: graph theoretical analysis of structural and functional systems , 2009, Nature Reviews Neuroscience.

[20]  Atsushi Uchida,et al.  Consistency of nonlinear system response to complex drive signals. , 2004, Physical review letters.

[21]  Lester Melie-García,et al.  Characterizing brain anatomical connections using diffusion weighted MRI and graph theory , 2007, NeuroImage.

[22]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[23]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[24]  H. Berendse,et al.  The application of graph theoretical analysis to complex networks in the brain , 2007, Clinical Neurophysiology.

[25]  C. Stam,et al.  Small-world networks and functional connectivity in Alzheimer's disease. , 2006, Cerebral cortex.

[26]  Edward T. Bullmore,et al.  Reproducibility of graph metrics of human brain functional networks , 2009, NeuroImage.

[27]  Olaf Sporns,et al.  Complex network measures of brain connectivity: Uses and interpretations , 2010, NeuroImage.

[28]  Sharon L. Milgram,et al.  The Small World Problem , 1967 .

[29]  V Latora,et al.  Efficient behavior of small-world networks. , 2001, Physical review letters.

[30]  Daniel L. Rubin,et al.  Network Analysis of Intrinsic Functional Brain Connectivity in Alzheimer's Disease , 2008, PLoS Comput. Biol..