Abstract
Studies on antisocial personality disorder (ASPD) subjects focus on brain functional alterations in relation to antisocial behaviors. Neuroimaging research has identified a number of focal brain regions with abnormal structures or functions in ASPD. However, little is known about the connections among brain regions in terms of inter-regional whole-brain networks in ASPD patients, as well as possible alterations of brain functional topological organization. In this study, we employ resting-state functional magnetic resonance imaging (R-fMRI) to examine functional connectome of 32 ASPD patients and 35 normal controls by using a variety of network properties, including small-worldness, modularity, and connectivity. The small-world analysis reveals that ASPD patients have increased path length and decreased network efficiency, which implies a reduced ability of global integration of whole-brain functions. Modularity analysis suggests ASPD patients have decreased overall modularity, merged network modules, and reduced intra- and inter-module connectivities related to frontal regions. Also, network-based statistics show that an internal sub-network, composed of 16 nodes and 16 edges, is significantly affected in ASPD patients, where brain regions are mostly located in the fronto-parietal control network. These results suggest that ASPD is associated with both reduced brain integration and segregation in topological organization of functional brain networks, particularly in the fronto-parietal control network. These disruptions may contribute to disturbances in behavior and cognition in patients with ASPD. Our findings may provide insights into a deeper understanding of functional brain networks of ASPD.
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References
Arfken, M. (2009). Brain, Mind, and Human Behavior in Contemporary Cognitive Science: Critical Assessments of the Philosophy of Psychology. Theory & Psychology, 19(6), 860–862.
Arnemann, K. L., Chen, A. J. W., Novakovic-Agopian, T., Gratton, C., Nomura, E. M., & D’Esposito, M. (2015). Functional brain network modularity predicts response to cognitive training after brain injury. Neurology, 84(15), 1568–1574.
Balenzuela, P., Chernomoretz, A., Fraiman, D., Cifre, I., Sitges, C., Montoya, P., et al. (2010). Modular organization of brain resting state networks in chronic back pain patients. Front Neuroinform, 4, 116, doi:10.3389/fninf.2010.00116.
Biswal, B. B., Mennes, M., Zuo, X. N., Gohel, S., Kelly, C., Smith, S. M., et al. (2010). Toward discovery science of human brain function. Proceeding of the National Academy of Science of the United States of Aamerica, 107(10), 4734–4739.
Blair, R. J., & Mitchell, D. G. (2009). Psychopathy, attention and emotion. Psychol Med, 39(4), 543–555.
Bonelli, R. M., & Cummings, J. L. (2007). Frontal-subcortical circuitry and behavior. Dialogues Clin Neurosci, 9(2), 141–151.
Brown, D., Larkin, F., Sengupta, S., Romero-Ureclay, J. L., Ross, C. C., Gupta, N., et al. (2014). Clozapine: an effective treatment for seriously violent and psychopathic men with antisocial personality disorder in a UK high-security hospital. CNS Spectrums, 19(5), 391–402.
Buckner, R. L., & Carroll, D. C. (2007). Self-projection and the brain. Trends Cogn Sci, 11(2), 49–57.
Bullmore, E. T., Suckling, J., Overmeyer, S., Rabe-Hesketh, S., Taylor, E., & Brammer, M. J. (1999). Global, voxel, and cluster tests, by theory and permutation, for a difference between two groups of structural MR images of the brain. IEEE Trans Med Imaging, 18(1), 32–42.
Campbell-Meiklejohn, D. K., Kanai, R., Bahrami, B., Bach, D. R., Dolan, R. J., Roepstorff, A., et al. (2012). Structure of orbitofrontal cortex predicts social influence. Curr Biol, 22(4), 123–124.
Caspers, S., Schleicher, A., Bacha-Trams, M., Palomero-Gallagher, N., Amunts, K., & Zilles, K. (2012). Organization of the Human Inferior Parietal Lobule Based on receptor architectonics. Cereb Cortex, 23(3), 615–628.
Cavanna, A. E., & Trimble, M. R. (2006). The precuneus: a review of its functional anatomy and behavioural correlates. Brain, 129(Pt 3), 564–583.
Cole, M. W., Repovs, G., & Anticevic, A. (2014). The frontoparietal control system: a central role in mental health. Neuroscientist, 20(6), 652–664.
de Oliveira-Souza, R., Hare, R. D., Bramati, I. E., Garrido, G. J., Ignacio, F. A., Tovar-Moll, F., et al. (2008). Psychopathy as a disorder of the moral brain: fronto-temporo-limbic grey matter reductions demonstrated by voxel-based morphometry. NeuroImage, 40(3), 1202–1213.
Demeter, E., Hernandez-Garcia, L., Sarter, M., & Lustig, C. (2011). Challenges to attention: a continuous arterial spin labeling (ASL) study of the effects of distraction on sustained attention. NeuroImage, 54(2), 1518–1529.
Dosenbach, N. U., Nardos, B., Cohen, A. L., Fair, D. A., Power, J. D., Church, J. A., et al. (2010). Prediction of individual brain maturity using fMRI. Science, 329(5997), 1358–1361.
Fazel, S., & Danesh, J. (2002). Serious mental disorder in 23000 prisoners: a systematic review of 62 surveys. Lancet, 359(9306), 545–550.
Fecteau, S., Pascual-Leone, A., Zald, D. H., Liguori, P., Theoret, H., Boggio, P. S., et al. (2007). Activation of prefrontal cortex by transcranial direct current stimulation reduces appetite for risk during ambiguous decision making. J Neurosci, 27(23), 6212–6218.
Fox, M. D., Zhang, D., Snyder, A. Z., & Raichle, M. E. (2009). The global signal and observed anticorrelated resting state brain networks. J Neurophysiol, 101(6), 3270–3283.
Gamboa, O. L., Tagliazucchi, E., von Wegner, F., Jurcoane, A., Wahl, M., Laufs, H., et al. (2014). Working memory performance of early MS patients correlates inversely with modularity increases in resting state functional connectivity networks. NeuroImage, 94, 385–395.
Guimera, R., & Amaral, L. A. N. (2005). Functional cartography of complex metabolic networks. Nature, 433(7028), 895–900.
Hawkins, K. M., Sayegh, P., Yan, X., Crawford, J. D., & Sergio, L. E. (2012). Neural Activity in Superior Parietal Cortex during Rule-based Visual-motor Transformations. J Cogn Neurosci, 25(3), 436–454.
Hoppenbrouwers, S. S., Nazeri, A., de Jesus, D. R., Stirpe, T., Felsky, D., Schutter, D. J., et al. (2013). White matter deficits in psychopathic offenders and correlation with factor structure. PLoS One, 8(8), e72375. doi:10.1371/journal.pone.0072375.
Jastorff, J., Clavagnier, S., Gergely, G., & Orban, G. A. (2011). Neural mechanisms of understanding rational actions: middle temporal gyrus activation by contextual violation. Cereb Cortex, 21(2), 318–329.
Koenigs, M., Barbey, A. K., Postle, B. R., & Grafman, J. (2009). Superior parietal cortex is critical for the manipulation of information in working memory. J Neurosci, 29(47), 14980–14986.
Kolb, B., & Whishaw, I. (1990). Fundamentals of human neuropsychology. New York: W.H. Freeman and Co.
Kumari, V., Uddin, S., Premkumar, P., Young, S., Gudjonsson, G. H., Raghuvanshi, S., et al. (2014). Lower anterior cingulate volume in seriously violent men with antisocial personality disorder or schizophrenia and a history of childhood abuse. Aust N Z J Psychiatry, 48(2), 153–161.
Latora, V., & Marchiori, M. (2001). Efficient behavior of small-world networks. Phys Rev Lett, 87(19). doi:10.1103/Physrevlett.87.198701.
Latora, V., & Marchiori, M. (2003). Economic small-world behavior in weighted networks. European. Physical Journal B, 32(2), 249–263.
Liu, H., Liao, J., Jiang, W., & Wang, W. (2014). Changes in low-frequency fluctuations in patients with antisocial personality disorder revealed by resting-state functional MRI. PLoS One, 9(3). doi:10.1371/journal.pone.0089790.
Lynall, M. E., Bassett, D. S., Kerwin, R., McKenna, P. J., Kitzbichler, M., Muller, U., et al. (2010). Functional connectivity and brain networks in schizophrenia. J Neurosci, 30(28), 9477–9487.
Maslov, S., & Sneppen, K. (2002). Specificity and stability in topology of protein networks. Science, 296(5569), 910–913.
Meshi, D., Biele, G., Korn, C. W., & Heekeren, H. R. (2012). How expert advice influences decision making. PLoS One, 7(11). doi:10.1371/journal.pone.0049748.
Meunier, D., Lambiotte, R., & Bullmore, E. T. (2010). Modular and hierarchically modular organization of brain networks. Front Neurosci, 4, 200. doi:10.3389/fnins.2010.00200.
Meyer, M. L., Masten, C. L., Ma, Y. N., Wang, C. B., Shi, Z. H., Eisenberger, N. I., et al. (2013). Empathy for the social suffering of friends and strangers recruits distinct patterns of brain activation. Soc Cogn Affect Neurosci, 8(4), 446–454.
Meyers, C. A., Berman, S. A., Scheibel, R. S., & Hayman, A. (1992). Case-Report - Acquired Antisocial Personality-Disorder Associated with Unilateral Left Orbital Frontal-Lobe Damage. J Psychiatry Neurosci, 17(3), 121–125.
Miller, B. L., Darby, A., Benson, D., Cummings, J., & Miller, M. (1997). Aggressive, socially disruptive and antisocial behaviour associated with fronto-temporal dementia. Br J Psychiatry, 170(2), 150–154.
Moffitt, T. E., Caspi, A., Harrington, H., & Milne, B. J. (2002). Males on the life-course-persistent and adolescence-limited antisocial pathways: follow-up at age 26 years. Dev Psychopathol, 14(1), 179–207.
Moore, T. L., Schettler, S. P., Killiany, R. J., Rosene, D. L., & Moss, M. B. (2009). Effects on executive function following damage to the prefrontal cortex in the rhesus monkey. Behav Neurosci, 123(2), 231–241.
Muller, J. L., Ganssbauer, S., Sommer, M., Dohnel, K., Weber, T., Schmidt-Wilcke, T., et al. (2008a). Gray matter changes in right superior temporal gyrus in criminal psychopaths. Evidence from voxel-based morphometry. Psychiatry Research-Neuroimaging, 163(3), 213–222.
Muller, J. L., Sommer, M., Dohnel, K., Weber, T., Schmidt-Wilcke, T., & Hajak, G. (2008b). Disturbed prefrontal and temporal brain function during emotion and cognition interaction in criminal psychopathy. ss, 26(1), 131–150.
Murphy, K., Birn, R. M., Handwerker, D. A., Jones, T. B., & Bandettini, P. A. (2009). The impact of global signal regression on resting state correlations: are anti-correlated networks introduced? Neuroimage, 44(3), 893–905.
Newman, M. E., & Girvan, M. (2004). Finding and evaluating community structure in networks. Phys Rev E, 69(2 Pt 2). doi:10.1103/PhysRevE.69.026113.
Newman, M. E. J. (2006). Modularity and community structure in networks. Proc Natl Acad Sci U S A, 103(23), 8577–8582.
Ogilvie, J. M., Stewart, A. L., Chan, R. C. K., & Shum, D. H. K. (2011). Neuropsychological measures of executive function and antisocial behavior: A Meta-Analysis. Criminology, 49(4), 1063–1107.
Onnela, J. P., Saramaki, J., Kertesz, J., & Kaski, K. (2005). Intensity and coherence of motifs in weighted complex networks. Phys Rev E, 71(6), doi:10.1103/Physreve.71.065103.
Peng, Z., Shi, F., Shi, C., Yang, Q., Chan, R. C., & Shen, D. (2014). Disrupted cortical network as a vulnerability marker for obsessive-compulsive disorder. Brain Struct Funct, 219(5), 1801–1812.
Philippi, C. L., Pujara, M. S., Motzkin, J. C., Newman, J., Kiehl, K. A., & Koenigs, M. (2015). Altered resting-state functional connectivity in cortical networks in psychopathy. J Neurosci, 35(15), 6068–6078.
Potegal, M. (2012). Temporal and frontal lobe initiation and regulation of the top-down escalation of anger and aggression. Behav Brain Res, 231(2), 386–395.
Power, J. D., Cohen, A. L., Nelson, S. M., Wig, G. S., Barnes, K. A., Church, J. A., et al. (2011). Functional Network Organization of the Human Brain. Neuron, 72(4), 665–678.
Radua, J., Phillips, M. L., Russell, T., Lawrence, N., Marshall, N., Kalidindi, S., et al. (2010). Neural response to specific components of fearful faces in healthy and schizophrenic adults. NeuroImage, 49(1), 939–946.
Raine, A., Lencz, T., Bihrle, S., LaCasse, L., & Colletti, P. (2000). Reduced prefrontal gray matter volume and reduced autonomic activity in antisocial personality disorder. Arch Gen Psychiatry, 57(2), 119–127.
Raine, A., Moffitt, T. E., Caspi, A., Loeber, R., Stouthamer-Loeber, M., & Lynam, D. (2005). Neurocognitive impairments in boys on the life-course persistent antisocial path. J Abnorm Psychol, 114(1), 38–49.
Rascovsky, K., Hodges, J. R., Knopman, D., Mendez, M. F., Kramer, J. H., Neuhaus, J., et al. (2011). Sensitivity of revised diagnostic criteria for the behavioural variant of frontotemporal dementia. Brain, 134(Pt 9), 2456–2477.
Reichardt, J., & Bornholdt, S. (2006). When are networks truly modular? Physica D-Nonlinear Phenomena, 224(1–2), 20–26.
Rubinov, M., & Sporns, O. (2010). Complex network measures of brain connectivity: uses and interpretations. NeuroImage, 52(3), 1059–1069.
Rubinov, M., , Sporns, O., van Leeuwen, C., & Breakspear, M. (2009). Symbiotic relationship between brain structure and dynamics. BMC Neurosci, 10. doi:10.1186/1471-2202-10-55.
Schneider, F., Habel, U., Kessler, C., Posse, S., Grodd, W., & Muller-Gartner, H. W. (2000). Functional imaging of conditioned aversive emotional responses in antisocial personality disorder. Neuropsychobiology, 42(4), 192–201.
Seguin, J. R., , Sylvers, P., & Lilienfeld, S. O. (2007). The Neuropsychology of Violence. Cambridge. Handbook of Violent Behavior and Aggression, 187–214.
Shi, F., , Wang, L., Peng, Z. W., Wee, C. Y., & Shen, D. G. (2013). Altered modular Organization of Structural Cortical Networks in children with autism. PLoS One, 8(5). doi:10.1371/journal.pone.0063131.
Shi, F., Yap, P. T., Gao, W., Lin, W., Gilmore, J. H., & Shen, D. (2012). Altered structural connectivity in neonates at genetic risk for schizophrenia: a combined study using morphological and white matter networks. NeuroImage, 62(3), 1622–1633.
Sporns, O. (2011). The human connectome: a complex network. Year in Cognitive Neuroscience, 1224, 109–125.
Sporns, O., & Zwi, J. D. (2004). The small world of the cerebral cortex. Neuroinformatics, 2(2), 145–162.
Stam, C. J. (2004). Functional connectivity patterns of human magnetoencephalographic recordings: a ‘small-world’ network? Neurosci Lett, 355(1–2), 25–28.
Sundram, F., Deeley, Q., Sarkar, S., Daly, E., Latham, R., Craig, M., et al. (2012). White matter microstructural abnormalities in the frontal lobe of adults with antisocial personality disorder. Cortex, 48(2), 216–229.
Supekar, K., Menon, V., Rubin, D., Musen, M., & Greicius, M. D. (2008). Network analysis of intrinsic functional brain connectivity in Alzheimer’s disease. PLoS Comput Biol, 4(6), e1000100.
Tagliazucchi, E., von Wegner, F., Morzelewski, A., Brodbeck, V., Borisov, S., Jahnke, K., et al. (2013). Large-scale brain functional modularity is reflected in slow electroencephalographic rhythms across the human non-rapid eye movement sleep cycle. NeuroImage, 70, 327–339.
Talati, A., & Hirsch, J. (2005). Functional specialization within the medial frontal gyrus for perceptual go/no-go decisions based on "what,” "when,” and "where” related information: An fMRI study. J Cogn Neurosci, 17(7), 981–993.
Tang, Y., Jiang, W., Liao, J., Wang, W., & Luo, A. (2013). Identifying individuals with antisocial personality disorder using resting-state FMRI. PLoS One, 8(4). doi:10.1371/journal.pone.0060652.
Tzourio-Mazoyer, N., Landeau, B., Papathanassiou, D., Crivello, F., Etard, O., Delcroix, N., et al. (2002). Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. NeuroImage, 15(1), 273–289.
Vaessen, M. J., Braakman, H. M. H., Heerink, J. S., Jansen, J. F. A., Debeij-van Hall, M. H. J. A., Hofman, P. A. M., et al. (2013). Abnormal modular Organization of Functional Networks in cognitively impaired children with frontal lobe epilepsy. Cereb Cortex, 23(8), 1997–2006.
Vincent, J. L., Kahn, I., Snyder, A. Z., Raichle, M. E., & Buckner, R. L. (2008). Evidence for a frontoparietal control system revealed by intrinsic functional connectivity. J Neurophysiol, 100(6), 3328–3342.
Vogt, B. A., & Laureys, S. (2005). Posterior cingulate, precuneal and retrosplenial cortices: cytology and components of the neural network correlates of consciousness. Prog Brain Res, 150, 205–217.
Volz, K. G., Schubotz, R. I., & von Cramon, D. Y. (2004a). Uncertainty in decision making and its neural correlates. J Psychophysiol, 18(4), 201–202.
Volz, K. G., Schubotz, R. I., & von Cramon, D. Y. (2004b). Why am I unsure? Internal and external attributions of uncertainty dissociated by fMRI. NeuroImage, 21(3), 848–857.
Walton, M. E., Behrens, T. E. J., Buckley, M. J., Rudebeck, P. H., & Rushworth, M. F. S. (2010). Separable learning Systems in the Macaque Brain and the role of orbitofrontal cortex in contingent learning. Neuron, 65(6), 927–939.
Wang, J., Zuo, X., Dai, Z., Xia, M., Zhao, Z., Zhao, X., et al. (2013). Disrupted functional brain connectome in individuals at risk for Alzheimer’s disease. Biol Psychiatry, 73(5), 472–481.
Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of ‘small-world’ networks. Nature, 393(6684), 440–442.
Wee, C. Y., Zhao, Z., Yap, P. T., Wu, G., Shi, F., Price, T., et al. (2014). Disrupted brain functional network in internet addiction disorder: a resting-state functional magnetic resonance imaging study. PLoS One, 9(9). doi:10.1371/journal.pone.0107306.
Widiger, T. A., & Costa Jr., P. T. (1994). Personality and personality disorders. J Abnorm Psychol, 103(1), 78–91.
Wolf, R. C., Pujara, M. S., Motzkin, J. C., Newman, J. P., Kiehl, K. A., Decety, J., et al. (2015). Interpersonal traits of psychopathy linked to reduced integrity of the uncinate fasciculus. Hum Brain Mapp, 36(10), 4202–4209.
Yan, C., & Zang, Y. (2010). DPARSF: A MATLAB toolbox for "pipeline" data analysis of resting-state fMRI. Front Syst Neurosci, 4, 13. doi:10.3389/fnsys.2010.00013.
Yang, Y., & Raine, A. (2009). Prefrontal structural and functional brain imaging findings in antisocial, violent, and psychopathic individuals: a meta-analysis. Psychiatry Res, 174(2), 81–88.
Zahn, R., Moll, J., Iyengar, V., Huey, E. D., Tierney, M., Krueger, F., et al. (2009). Social conceptual impairments in frontotemporal lobar degeneration with right anterior temporal hypometabolism. Brain, 132, 604–616.
Zalesky, A., Fornito, A., & Bullmore, E. T. (2010). Network-based statistic: identifying differences in brain networks. NeuroImage, 53(4), 1197–1207.
Zhang, J., Wang, J., Wu, Q., Kuang, W., Huang, X., He, Y., et al. (2011). Disrupted brain connectivity networks in drug-naive, first-episode major depressive disorder. Biol Psychiatry, 70(4), 334–342.
Acknowledgments
We thank all the volunteers for their participation in the study and the anonymous referees for their insightful comments and suggestions. The Funding Project of Education Ministry for the Development of Liberal Arts and Social Sciences (13YJCZH068), the China Postdoctoral Science Foundation (2015 M582879) and Key Laboratory of Basic Education Information Technology of Hunan Province (2015TP1017) helped support this work. Additionally, this study was partially supported by the National Natural Science Foundation of China (61420106001, 61375111, 81571298) and, in part, supported by NIH grants (AG041721, EB006733, EB008374, EB009634).
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All authors declare that they have no conflict of interest. All procedures followed are in accordance with the ethical standards of the responsible committee on human experimentation (institutional and national) and with the Helsinki Declaration of 1975, and the applicable revisions at the time of the investigation. Written informed consent was obtained from all patients included in the study.
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Weixiong Jiang and Feng Shi are co-first authors.
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Appendix
Small-world Analysis
The small-world architectures of a network could be obtained by calculating clustering coefficient and characteristic path length (Watts and Strogatz 1998). For a weighted network N the clustering coefficient C w is the average of all nodal clustering coefficients, where nodal clustering coefficient \( {C}_i^w \) for a given node i is defined as (Onnela et al. 2005):
Where n is the number of nodes, k i is the degree of node i, i.e., the number of non-zero connections, w ij is connection weights between node i and node j. The clustering coefficient quantifies the extent of local interconnectivity or cliquishness of a network. The characteristic path length L w of a weighted network N with n nodes is defined as:
where \( {d}_{ij}^w \) is the weighted shortest path length between node i and node j and is computed as the smallest sum of the edge lengths throughout all of the possible paths in the network from node i and node j. The characteristic path length reflects the mean distance or routing efficiency between any given pair of nodes.
Their normalized versions (\( {\overset{\sim }{\mathrm{C}}}^{\mathrm{W}},{\overset{\sim }{\mathrm{L}}}^{\mathrm{W}} \)) were obtained using random networks, i.e., dividing the real values C wand LW by the corresponding mean derived from 100 random networks that preserved the same number of nodes, edges and degree distributions as the real brain networks (Maslov and Sneppen 2002; Sporns and Zwi 2004). During the random rewiring procedure, we specially retained the weight of each edge. A small-world network typically shows \( {\overset{\sim }{C}}^w>1 \) and \( {\overset{\sim }{L}}^w\approx 1 \) (Watts and Strogatz 1998).
Network Efficiency
Network efficiency metrics can be used to provide more biologically sensible properties for brain networks. The global efficiency (\( {E}_{glob}^w \)) and local efficiency (\( {E}_{loc}^w \)) quantify the extent of information transmission at the global network and the individual node levels, respectively (Latora and Marchiori 2001). For a network N with n nodes and k edges, the global efficiency of N can be computed as:
where \( {d}_{ij}^w \) is the shortest path length between node i and node j in N. Global efficiency measures the extent of parallel information transmission at the global network. The local efficiency of G is measured as:
where \( {E}_{glob}^w\left({N}_i\right) \) is the global efficiency of N i , the subgraph composed of the neighbors of node i. Local efficiency quantifies the fault tolerance of the network.
Modularity
Modularity is an important organizational principle for brain networks (Meunier et al. 2010). According to Newman’s algorithm (Newman 2004), the modularity index Qw of a weighted network is defined as
Where 푙w is the sum of all weights in the network, w ij is connection weights between node i and node j, k i is the degree of node i, i.e., the number of non-zero connections, m i is the module containing node 푖, and \( {\delta}_{m_i,{m}_j}=1 \) if m i = m j , and 0 otherwise. Modularity quantifies the extent of modular organization. The aim of the module identification process is to find a specific partition that yields the largest network modularity, \( {\overset{\sim }{\mathrm{Q}}}_{\max } \).
To assess the inter- and intra-modular connectivities, we calculated the participation coefficient (PC) and intra-module degree (MD) for each node to detect the inter- and intra-module connection density (Guimera and Amaral 2005). For a weighted network, participation coefficient is defined as:
where 푀 is the set of modules and \( {k}_i^w(m) \) is the weight of links between i and all nodes in module m. For a weighted network, weighted within-module degree z-score is define
where m i is the module containing node i, \( {k}_i^w\left({m}_i\right) \)is the within-module degree of i (the number of links between i and all other nodes in m i ), and \( {\overset{-}{k}}^w\left({m}_i\right) \)and \( {\sigma}^{k^w\left({m}_i\right)} \)are the respective mean and standard deviation of the within-module m i degree distribution.
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Jiang, W., Shi, F., Liao, J. et al. Disrupted functional connectome in antisocial personality disorder. Brain Imaging and Behavior 11, 1071–1084 (2017). https://doi.org/10.1007/s11682-016-9572-z
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DOI: https://doi.org/10.1007/s11682-016-9572-z