  A complex network approach on a rough fracture is developed. In this manner,
some hidden metric spaces (similarity measurements) between apertures profiles
are set up and a general evolutionary network in two directions (in parallel
and perpendicular to the shear direction) is constructed. Also, an algorithm
(COmplex Networks on Apertures: CONA) is proposed in which evolving of a
network is accomplished using preferential detachments and attachments of edges
(based on a competition and game manner) while the number of nodes is fixed.
Also, evolving of clustering coefficients and number of edges display similar
patterns as well as are appeared in shear stress, hydraulic conductivity and
dilation changes, which can be engaged to estimate shear strength distribution
of asperities.
