Experimental Brain Research

, Volume 236, Issue 10, pp 2677–2689 | Cite as

Small-world indices via network efficiency for brain networks from diffusion MRI

  • Lan LinEmail author
  • Zhenrong Fu
  • Cong Jin
  • Miao Tian
  • Shuicai Wu
Research Article


The small-world architecture has gained considerable attention in anatomical brain connectivity studies. However, how to adequately quantify small-worldness in diffusion networks has remained a problem. We addressed the limits of small-world measures and defined new metric indices: the small-world efficiency (SWE) and the small-world angle (SWA), both based on the tradeoff between high global and local efficiency. To confirm the validity of the new indices, we examined the behavior of SWE and SWA of networks based on the Watts–Strogatz model as well as the diffusion tensor imaging (DTI) data from 75 healthy old subjects (aged 50–70). We found that SWE could classify the subjects into different age groups, and was correlated with individual performance on the WAIS-IV test. Moreover, to evaluate the sensitivity of the proposed measures to network, two network attack strategies were applied. Our results indicate that the new indices outperform their predecessors in the analysis of DTI data.


Small world Connectome DTI Brain network 



The authors would like to thank the anonymous reviewers for their helpful suggestions and appreciate professor Zalesky from the University of Melbourne and Melbourne Health for sharing the uniform parcellation algorithm. This work was supported by Grants from the Scientific Research General Project of Beijing Municipal Education Committee (KM201810005033), the Natural Science Foundation of Beijing (7143171) and the National Key Technology Support Program of China (2015BAI02B03).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Lan Lin
    • 1
    Email author
  • Zhenrong Fu
    • 1
  • Cong Jin
    • 2
  • Miao Tian
    • 1
  • Shuicai Wu
    • 1
  1. 1.Biomedical Research Center, College of Life Science and BioengineeringBeijing University of TechnologyBeijingChina
  2. 2.Medical Engineering Department, Beijing Friendship HospitalCapital Medical UniversityBeijingChina

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