Complex functional brain networks are large networks of brain regions and
functional brain connections. Statistical characterizations of these networks
aim to quantify global and local properties of brain activity with a small
number of network measures. Important functional network measures include
measures of modularity (measures of the goodness with which a network is
optimally partitioned into functional subgroups) and measures of centrality
(measures of the functional influence of individual brain regions).
Characterizations of functional networks are increasing in popularity, but are
associated with several important methodological problems. These problems
include the inability to characterize densely connected and weighted functional
networks, the neglect of degenerate topologically distinct high-modularity
partitions of these networks, and the absence of a network null model for
testing hypotheses of association between observed nontrivial network
properties and simple weighted connectivity properties. In this study we
describe a set of methods to overcome these problems. Specifically, we
generalize measures of modularity and centrality to fully connected and
weighted complex networks, describe the detection of degenerate high-modularity
partitions of these networks, and introduce a weighted-connectivity null model
of these networks. We illustrate our methods by demonstrating degenerate
high-modularity partitions and strong correlations between two complementary
measures of centrality in resting-state functional magnetic resonance imaging
(MRI) networks from the 1000 Functional Connectomes Project, an open-access
repository of resting-state functional MRI datasets. Our methods may allow more
sound and reliable characterizations and comparisons of functional brain
networks across conditions and subjects.

本研究通过总结一些方法，对完全联通和加权的复杂网络中的模块度和中心度进行了推广，并介绍了这些网络的加权连通性空模型。通过运用这些方法，本研究展示了在来自 1000 个功能连接组项目的静息态功能性磁共振成像（MRI）网络中的退化高模块度划分和中心度的两个互补测量之间的强相关性。这些方法可能使得跨条件和受试者比较的功能性大脑网络的特性更加牢固和可靠。