Degree-preserving edge rewiring
= Degree-preserving edge rewiring
<Degree-preserving edge rewiring> replaces two <edges> $(u,v)$ and $(x,y)$ by $(u,y)$ and $(x,v)$, preserving every endpoint's <degree of a vertex>. On <simple graphs>, reject proposed <self-loops> and duplicate edges. Symmetric random proposals with rejected moves retained preserve a uniform distribution on the reachable realizations; adequate mixing remains a separate requirement. Connectivity can change unless explicitly constrained.