Ensuring high network reliability is of utmost importance, especially as the number of networked computers increases. Connectivity is an important factor in measuring how reliable a network is. Intuitively, the higher the connectivity, the lower the chances that a failure results in isolated computers. However, the traditional definition of connectivity in graph theory does not seem appropriate for computer networks since it is not likely that all of the neighbors of a computer fail at the same time.

Zhou and Xu report extensively on the many proposals in the literature to provide better definitions of connectivity. Unfortunately, there are many definitions and network topologies for which there is not an analytical characterization of connectivity. The authors report on their findings regarding characterizing so-called R¹ and R² connectivity for (n, k)-arrangement networks.

The authors have managed to present the many related proposals in the literature in an easy-to-understand manner. Even researchers who are not familiar with this field will be able to easily follow the argumentation and understand the results. They will also see that the literature only provides partial results to calculate connectivity analytically. Unfortunately, Zhou and Xu’s results are partial, too, which means that this research field is far from closed.