Frontiers in Systems Neuroscience www.frontiersin.org June 2010 | Volume 4 | Article 16 | 1 SYSTEMS NEUROSCIENCE Review ARticle published: 07 June 2010 doi: 10.3389/fnsys.2010.00016 (Zang et al., 2004), network homogeneity (Uddin et al., 2008), amplitude of low-frequency fluctuations (ALFF) (Zang et al., 2007), fractional ALFF (Zou et al., 2008) and fractal complexity (Wink et al., 2006). In contrast, the other measures the relationship between different brain units (i.e., highly coherent spontaneous fluctuations or functional connectivity), such as seed-based func- tional connectivity analysis (Biswal et al., 1995), clustering (Cordes et al., 2002) and independent component analysis (ICA) (van de Ven et al., 2004). Connectivity-based methods have been widely used to detect functionally connected brain networks, including motor (Biswal et al., 1995), auditory (Cordes et al., 2001), visual (Lowe et al., 1998), language (Hampson et al., 2002), default-mode (Greicius et al., 2003), and attention systems (Fox et al., 2006). These brain networks have demonstrated high consistency and reproduc- ibility across subjects and sessions (Damoiseaux et al., 2006 Chen et al., 2008a Meindl et al., 2009 Zuo et al., 2010a), high test���retest reliability (Shehzad et al., 2009 Zuo et al., 2010a), high reproduc- ibility across different analytic approaches (Long et al., 2008 Franco et al., 2009) and a striking correspondence to task activation maps (Smith et al., 2009). More recently, using novel graph theory-based approaches, these identified biologically plausible brain networks were found to topologically organize in a non-trivial manner (e.g., small-world architecture and modular structure) that support effi- cient information processing of the brain. Graph theory-based approaches model the brain as a complex network represented graphically by a collection of nodes and edges. In the virtual graph, nodes indicate anatomical elements IntroductIon As a novel, non-invasive way to measure spontaneous neural activity in the human brain, resting-state functional magnetic resonance imaging (R-fMRI) has attracted considerable atten- tion (Biswal et al., 1995 Fox and Raichle, 2007). R-fMRI measures the endogenous or spontaneous brain activity as low-frequency fluctuations in blood oxygen level-dependent (BOLD) signals. This low-frequency fluctuation phenomenon is vital for a better understanding of human brain function because extremely dis- proportionate energy consumption appears within the regions showing high resting metabolisms (Raichle et al., 2001 Raichle, 2006). Beginning with a seminal demonstration of highly coherent low-frequency fluctuations within the brain motor system (Biswal et al., 1995), R-fMRI has been extensively used to investigate nor- mal brain function (Greicius et al., 2003 Beckmann et al., 2005 Fox et al., 2005 Margulies et al., 2007 Di Martino et al., 2008 Roy et al., 2009 Smith et al., 2009 Yan et al., 2009b), trait variability and behavioral characteristics (Hampson et al., 2006 Fox et al., 2007 Hesselmann et al., 2008 Kelly et al., 2008 Di Martino et al., 2009 Yan et al., 2009a), as well as various clinical populations (for reviews, see Greicius, 2008 Broyd et al., 2009 Zhang and Raichle, 2010). To date, many R-fMRI methods have been developed to explore the nature of resting-state brain. Currently, there are two main types of R-fMRI methods used to characterize spontaneous brain activity. One measures specific regional characteristics of R-fMRI signals within a brain region (e.g., voxels or parcellation units), such as regional homogeneity Graph-based network analysis of resting-state functional MRI Jinhui Wang1, Xinian Zuo2 and Yong He1* 1 State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing, China 2 Phyllis Green and Randolph C��wen Institute for Pediatric Neuroscience, New York University Langone Medical Center, New York, NY, USA In the past decade, resting-state functional MRI (R-fMRI) measures of brain activity have attracted considerable attention. Based on changes in the blood oxygen level-dependent signal, R-fMRI offers a novel way to assess the brain���s spontaneous or intrinsic (i.e., task-free) activity with both high spatial and temporal resolutions. The properties of both the intra- and inter-regional connectivity of resting-state brain activity have been well documented, promoting our understanding of the brain as a complex network. Specifically, the topological organization of brain networks has been recently studied with graph theory. In this review, we will summarize the recent advances in graph-based brain network analyses of R-fMRI signals, both in typical and atypical populations. Application of these approaches to R-fMRI data has demonstrated non-trivial topological properties of functional networks in the human brain. Among these is the knowledge that the brain���s intrinsic activity is organized as a small-world, highly efficient network, with significant modularity and highly connected hub regions. These network properties have also been found to change throughout normal development, aging, and in various pathological conditions. The literature reviewed here suggests that graph-based network analyses are capable of uncovering system-level changes associated with different processes in the resting brain, which could provide novel insights into the understanding of the underlying physiological mechanisms of brain function. We also highlight several potential research topics in the future. Keywords: resting-state, functional connectivity, human connectome, small-world, functional MRI, graph theory, brain, network Edited by: Lucina Q. Uddin, Stanford University, USA Reviewed by: Sophie Achard, University of Cambridge, UK Edward T. Bullmore, University of Cambridge, UK Alex Fornito, University of Melbourne, Australia *Correspondence: Yong He, State Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing, China. e-mail: yong.he@bnu.edu.cn

Frontiers in Systems Neuroscience www.frontiersin.org June 2010 | Volume 4 | Article 16 | 2 Wang et al. Graph theoretical analysis of resting fMRI (e.g., brain regions), and edges represent the relationships between nodes (e.g., connectivity). After the network modeling procedure, various graph theoretical metrics can be used to investigate the organizational mechanism underlying the relevant networks. In contrast to those widely used R-fMRI analytic methods (e.g., ALFF, seed-based functional connectivity and ICA), the graph- based network analyses allow us not only to visualize the overall connectivity pattern among all the elements of the brain (e.g., brain regions) but also to quantitatively characterize the global organization. In addition, this approach also gives insight into the topological reconfiguration of the brain in response to external task modulation (Eguiluz et al., 2005 Pachou et al., 2008 Bassett et al., 2009 Micheloyannis et al., 2009 Wang et al., 2010) or pathological attacks (for reviews, see Bassett and Bullmore, 2009 and He et al., 2009a). Moreover, it provides a vital framework to elucidate the relationship between brain structure and func- tion (Honey et al., 2010). Both structural and functional brain networks have been demonstrated to organize intrinsically as highly modular small-world architectures capable of efficiently transferring information at a low wiring cost as well as formatting highly connected hub regions (Salvador et al., 2005 Achard et al., 2007 He et al., 2007, 2009b Chen et al., 2008b Hagmann et al., 2008 Gong et al., 2009a). Furthermore, the utility of graph-based techniques has been proven by an increasing number of studies to probe potential mechanisms involved in normal development (Fair et al., 2007, 2008, 2009 Supekar et al., 2009), aging (Achard and Bullmore, 2007 Gong et al., 2009b Meunier et al., 2009a Micheloyannis et al., 2009 Wang et al., 2010), and various brain disorders (Stam et al., 2007 He et al., 2008, 2009c Liu et al., 2008 Supekar et al., 2009 Wang et al., 2009b Buckner et al., 2009). Given the lack of relevant reviews that focus exclusively on graph-based brain network research using R-fMRI, the purpose of the present review is to increase multi-discipline apprecia- tion and cooperation on this burgeoning field. In addition, this work provides the opportunity to revolutionize our view of brain organization and function by re-examining the progress made in this field. In this review, we will summarize the recent progress made in the study of functional brain networks constructed by intrinsic brain activity measured by R-fMRI. The paper is organized to three main sections. First, some basic concepts regarding brain connectiv- ity and graph theoretical approaches are introduced, along with a review of recent graph-based work on revealing the normal topo- logical architecture and underlying organization of functional brain networks. Then, we survey various R-fMRI applications of graph- based approaches to uncover changes in the network properties of brain development, aging and disorders. Finally, we highlight some technical challenges and future directions in this rapidly emerging research area. BasIc conceptIons BraIn connectIvIty networks A network is a collection of nodes and edges, where nodes indi- cate basic elements within the system of interest and edges indi- cate the associations among those elements. An accurate method for defining the most essential elements of a network (i.e., nodes and edges) is vital for network construction. Specifically, for brain networks, they can be described at different spatial levels, such as microscale, mesoscale, and macroscale or large-scale (Sporns et al., 2005). Given technical limitations and computational demand, most current studies focus on the macroscale or large-scale brain networks. In this review, we will also concentrate on the macroscale brain networks. In a macroscale brain network, nodes can be defined as EEG electrodes, MEG channels, or regions of interest (ROI) derived from anatomical atlases in MRI. After the definition of nodes, the edges among nodes can be defined by the functional or structural associations among different neuronal elements of the brain. To date, functional associations are measured by either the temporal correlation between spatially remote neurophysiological events, often referred to as the functional connectivity, or the influence that one neural system exerts over another, also termed effective connectivity (Friston et al., 1993). Structural associations can be measured by examining either direct diffusion-based anatomical connectivity or indirect morphology-based statistical interdepend- encies across populations (Bullmore and Sporns, 2009 He and Evans, 2010). Once these two basic elements of a network, nodes and edges, are extracted from the dataset, the constructed brain connectivity network can be further characterized using graph theoretical approaches. Figure 1 illustrates the schematic repre- sentation of network constructions using R-fMRI. Graph theoretIcal approaches Graph theory is the natural framework for the exact mathe- matical representation of complex networks. Formally, a com- plex network can be represented as a graph by G(N, K), with N denoting the number of nodes and K the number of edges in graph G. Graphs can be classified as directed or undirected based on whether the edges have sense of direction information. Likewise, graphs can also be divided into unweighted (binary) graphs if every edge in the graph has an equal weight of 1 or weighted graphs if its edges are assigned with different strengths. In this review, we will only focus on undirected and unweighted graphs. The descriptions for other types of graphs can be found in previous literature (Boccaletti et al., 2006 Bang-Jensen and Gutin, 2008). For an undirected and unweighted graph G(N, K), the con- nectivity pattern can be completely described by an N �� N sym- metric square matrix named adjacency matrix A whose entry a ij (i,j = 1,���,N) is 1 if there exists an edge between node i and j or 0 if one does not. Now we will list some important metrics that are frequently used in the field of neuroscience. Degree and degree distribution In a graph G(N, K), the degree of node i is the number of edges linked to it and is calculated as ki j = ���aij ���G , where aij is the ith row and jth column element of adjacency matrix A. Degree is a simple measurement for the connectivity of a node with the rest of the nodes in a network. The mean of degrees over all the nodes in G, referred to as the average degree, measures the extent to which the graph is connected. The degree distribution P(k) is defined as the probability that a node chosen uniformly at random has degree k or, equivalently, as the fraction of nodes in the graph having degree k. In terms of the form of degree distribution,