  Individual differences in brain functional networks may be related to complex
personal identifiers, including health, age, and ability. Understanding and
quantifying these differences is a necessary first step towards developing
predictive methods derived from network topology. Here, we present a method to
quantify individual differences in brain functional dynamics by applying
hypergraph analysis, a method from dynamic network theory. Using a summary
metric derived from the hypergraph formalism---hypergraph cardinality---we
investigate individual variations in two separate and complementary data sets.
The first data set ("multi-task") consists of 77 individuals engaging in four
consecutive cognitive tasks. We observed that hypergraph cardinality exhibits
variation across individuals while remaining consistent within individuals
between tasks; moreover, one of the memory tasks evinced a marginally
significant correspondence between hypergraph cardinality and age. This finding
motivated a similar analysis of the second data set ("age-memory"), in which 95
individuals of varying ages performed a memory task with a similar structure to
the multi-task memory task. With the increased age range in the age-memory data
set, the correlation between hypergraph cardinality and age correspondence
becomes significant. We discuss these results in the context of the well-known
finding linking age with network structure, and suggest that age-related
changes in brain function can be better understood by taking an integrative
approach that incorporates information about the dynamics of functional
interactions.
