To cut or not to cut? Assessing the modular structure of brain networks.
A wealth of methods has been developed to identify natural divisions of brain networks into groups or modules, with one of the most prominent being modularity. Compared with the popularity of methods to detect community structure, only a few methods exist to statistically control for spurious modules, relying almost exclusively on resampling techniques. It is well known that even random networks can exhibit high modularity because of incidental concentration of edges, even though they have no underlying organizational structure. Consequently, interpretation of community structure is confounded by the lack of principled and computationally tractable approaches to statistically control for spurious modules. In this paper we show that the modularity of random networks follows a transformed version of the Tracy-Widom distribution, providing for the first time a link between module detection and random matrix theory. We compute parametric formulas for the distribution of modularity for random networks as a function of network size and edge variance, and show that we can efficiently control for false positives in brain and other real-world networks.
McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. Electronic address: yutengchang@gmail.com.
Yu-Teng
YT
Chang
McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
Dimitrios
D
Pantazis
Signal and Image Processing Institute, University of Southern California, Los Angeles, CA 90089, USA.
Richard M
RM
Leahy
D000465:Algorithms; D001921:Brain / Q000033:anatomy & histology*; D016000:Cluster Analysis; D003198:Computer Simulation; D005189:False Positive Reactions; D006801:Humans; D007091:Image Processing, Computer-Assisted; D008959:Models, Neurological; D009010:Monte Carlo Method; D009415:Nerve Net / Q000033:anatomy & histology*; D059906:Neuroimaging / Q000379:methods*; D016011:Normal Distribution
Community structure; Functional connectivity; Graph partitioning methods; Modularity; Random graphs