Network measures

An individual network measure may characterize one or several aspects of global and local brain connectivity. The Brain Connectivity Toolbox contains measures that variously detect aspects of functional integration and segregation, quantify importance of individual brain regions, characterize patterns of local anatomical circuitry, and test resilience of networks to insult. The figure below illustrates some basic network measures, while the table below contains mathematical definitions of many measures.

Network measures are often represented in multiple ways. Thus, measures of individual network elements (such as nodes or links) typically quantify connectivity profiles associated with these elements and hence reflect the way in which these elements are embedded in the network. Measurement values of all individual elements comprise a distribution, which provides a more global description of the network. This distribution is most commonly characterized by its mean, although other features, such as distribution shape, may be more important if the distribution is nonhomogeneous. In addition to these different representations, network measures also have binary and weighted, directed and undirected variants. Weighted and directed variants of measures are typically generalizations of binary undirected variants and therefore reduce to the latter when computed on binary undirected networks.

Mathematical definitions of many toolbox measures: table.

Illustration of some toolbox measures (full list of measures).

Text, table and figure from: Rubinov M, Sporns O (2010) NeuroImage 52:1059-69.