The DOI matches its Crossref record; 67 of the 67 references it cites were found in a registry or an index.
Small-World Propensity and Weighted Brain Networks
Open accessAbstract
Quantitative descriptions of network structure can provide fundamental insights into the function of interconnected complex systems. Small-world structure, diagnosed by high local clustering yet short average path length between any two nodes, promotes information flow in coupled systems, a key function that can differ across conditions or between groups. However, current techniques to quantify small-worldness are density dependent and neglect important features such as the strength of network connections, limiting their application in real-world systems. Here, we address both limitations with a novel metric called the Small-World Propensity (SWP). In its binary instantiation, the SWP provides an unbiased assessment of small-world structure in networks of varying densities. We extend this concept to the case of weighted brain networks by developing (i) a standardized procedure for generating weighted small-world networks, (ii) a weighted extension of the SWP, and (iii) a method for mapping observed brain network data onto the theoretical model. In applying these techniques to compare real-world brain networks, we uncover the surprising fact that the canonical biological small-world network, the C. elegans neuronal network, has strikingly low SWP. These metrics, models, and maps form a coherent toolbox for the assessment and comparison of architectural properties in brain networks.
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Cites
Collective dynamics of ‘small-world’ networks
Watts, D. J., & Strogatz, S. H. (1998) · Nature · doi:10.1038/30918 · Cited by 43,060
Complex network measures of brain connectivity: Uses and interpretations
Rubinov, M., & Sporns, O. (2010) · NeuroImage · doi:10.1016/j.neuroimage.2009.10.003 · Cited by 11,522
Network motifs: simple building blocks of complex networks.
Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., & Alon, U. (2002) · Science · doi:10.1126/science.298.5594.824 · Cited by 7,368
Newman, M. (2010) · doi:10.1093/acprof:oso/9780199206650.001.0001 · Cited by 6,595
A General Framework for Weighted Gene Co-Expression Network Analysis
Zhang, B., & Horvath, S. (2005) · Statistical Applications in Genetics and Molecular Biology · doi:10.2202/1544-6115.1128 · Cited by 5,684
Uncovering the overlapping community structure of complex networks in nature and society
Palla, G., Derényi, I., Farkas, I., & Vicsek, T. (2005) · Nature · doi:10.1038/nature03607 · Cited by 5,373
The architecture of complex weighted networks
Barrat, A., Barthélemy, M., Pastor-Satorras, R., & Vespignani, A. (2004) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0400087101 · Cited by 4,218
Node centrality in weighted networks: Generalizing degree and shortest paths
Opsahl, T., Agneessens, F., & Skvoretz, J. (2010) · Social Networks · doi:10.1016/j.socnet.2010.03.006 · Cited by 3,718
Synchronization in complex networks
Arenas, A., Díaz-Guilera, A., Kurths, J., Moreno, Y., & Zhou, C. (2008) · Physics Reports · doi:10.1016/j.physrep.2008.09.002 · Cited by 3,713
Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality
Newman, M. E. J. (2001) · Physical Review E · doi:10.1103/physreve.64.016132 · Cited by 2,613
Cited by
Farahani, F. V., Karwowski, W., & Lighthall, N. R. (2019) · Frontiers in Neuroscience · doi:10.3389/fnins.2019.00585 · Cited by 718
Cognitive Network Neuroscience
Medaglia, J. D., Lynall, M.-E., & Bassett, D. S. (2015) · Journal of Cognitive Neuroscience · doi:10.1162/jocn_a_00810 · Cited by 419
Self-citationFrom maps to multi-dimensional network mechanisms of mental disorders
Braun, U., Schaefer, A., Betzel, R. F., Tost, H., Meyer-Lindenberg, A., & Bassett, D. S. (2018) · Neuron · doi:10.1016/j.neuron.2017.11.007 · Cited by 177
Self-citationOptimal trajectories of brain state transitions
Gu, S., Betzel, R. F., Mattar, M. G., Cieslak, M., Delio, P. R., Grafton, S. T., Pasqualetti, F., & Bassett, D. S. (2017) · NeuroImage · doi:10.1016/j.neuroimage.2017.01.003 · Cited by 183
Self-citationStability of graph theoretical measures in structural brain networks in Alzheimer’s disease
Mårtensson, G., Pereira, J. B., Mecocci, P., Vellas, B., Tsolaki, M., Kłoszewska, I., Soininen, H., Lovestone, S., Simmons, A., Volpe, G., et al. (2018) · Scientific Reports · doi:10.1038/s41598-018-29927-0 · Cited by 60
Metadata
- Authors
- Muldoon, S. F., Bridgeford, E. W., & Bassett, D. S.
- Venue
- Scientific Reports
- Published
- 2016-02-25
- Volume
- 6
- Issue
- 1
- Pages
- 22057-22057
- ISSN
- 2045-2322 (ISSN-L)
- OpenAlex
- W2411622228
- Cited by
- 304
- References
- 67
- FWCI
- 15.18
- Type
- journal article
- Language
- en
- Open access
- gold
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