  We propose a new unbiased threshold for network analysis named the
Cluster-Span Threshold (CST). This is based on the clustering coefficient, C,
following logic that a balance of `clustering' to `spanning' triples results in
a useful topology for network analysis and that the product of complementing
properties has a unique value only when perfectly balanced. We threshold
networks by fixing C at this balanced value, rather than fixing connection
density at an arbitrary value, as has been the trend. We compare results from
an electroencephalogram data set of volunteers performing visual short term
memory tasks of the CST alongside other thresholds, including maximum spanning
trees. We find that the CST holds as a sensitive threshold for distinguishing
differences in the functional connectivity between tasks. This provides a
sensitive and objective method for setting a threshold on weighted complete
networks which may prove influential on the future of functional connectivity
research.

Neurons and Cognition