  Our goal is to describe superconformal structures on super Riemann surfaces
(SRS), based on data assigned to a fatgraph. We start from the complex
structures on punctured $(1|1)$-supermanifolds, characterizing the
corresponding moduli and the deformations using Strebel differentials and
certain \v{C}ech cocycles for a specific covering, which we reproduce from a
fatgraph data, consisting of $U(1)$-graph connection and odd parameters at the
vertices. Then we consider dual $(1|1)$-supermanifolds and related
superconformal structures for $N=2$ super Riemann surfaces. The superconformal
structures $N=1$ SRS are computed as the fixed points of involution on
supermoduli space of $N=2$ SRS.
