The goal of the Cuthill-Mckee (and reverse Cuthill-Mckee) ordering algorithm is to reduce the bandwidth of a graph by reordering the indices assigned to each vertex. The Cuthill-Mckee ordering algorithm works by a local minimization of the i-th bandwidths. The vertices are basically assigned a breadth-first search order, except that at each step, the adjacent vertices are placed in the queue in order of increasing degree.
Below is an animation for visualisation of Cuthill-Mckee (and reverse Cuthill-Mckee) ordering algorithm.
In the below gif following color represents different states of node:
grey - unvisited
yellow - being visited
green - visited
