  Combinatorial methods are developed to find the cluster coordinates for
moduli space of flat connections which is describing the Coulomb branch of
higher rank N=2 theories derived by compactifying six dimensional (2,0) theory
on a punctured Riemann surface. The construction starts with a triangulation of
the punctured Riemann surface and a further tessellation of all the triangles.
The tessellation is used to construct a bipartite network from which a quiver
can be read straightforwardly. We prove that the quivers for different
triangulations are related by quiver mutations and justify that these are
really the cluster coordinates. These coordinates are important in studying BPS
wall crossing, line operators, and surface operators of these theories; and
they are also useful in exploring three dimensional Chern-Simons theory and the
corresponding N=2 gauge theory, two dimensional integrable system, etc.}
