brainconn.core.core_periphery_dir

core_periphery_dir(W, gamma=1, C0=None)

The optimal core/periphery subdivision is a partition of the network into two nonoverlapping groups of nodes, a core group and a periphery group. The number of core-group edges is maximized, and the number of within periphery edges is minimized.

The core-ness is a statistic which quantifies the goodness of the optimal core/periphery subdivision (with arbitrary relative value).

The algorithm uses a variation of the Kernighan-Lin graph partitioning algorithm to optimize a core-structure objective described in Borgatti & Everett (2000) Soc Networks 21:375-395

See Rubinov, Ypma et al. (2015) PNAS 112:10032-7

Parameters:

• W (NxN numpy.ndarray) – directed connection matrix
• gamma (core-ness resolution parameter) – Default value = 1 gamma > 1 detects small core, large periphery 0 < gamma < 1 detects large core, small periphery
• C0 (NxN numpy.ndarray) – Initial core structure