Abstract: A method and apparatus are presented for tolerating up to k faults in d-dimensional mesh architectures based on the approach of adding spare components (nodes) and extra links (edges) to a given target mesh where exactly k spare nodes are added and the number of links per node (degree of the mesh) is kept to a minimum. The resulting architecture can be reconfigured, without the use of switches, as an operable target mesh in the presence of up to k faults. According to one aspect of the invention, given a d-dimensional mesh architecture M having N=n.sub.1 .times.n.sub.2 x . . . x n.sub.d nodes, the fault tolerant mesh can be represented by a circulant graph having exactly N+k nodes. This graph has the property that given any set of k or fewer faulty nodes, the remaining graph, after the performance of a predetermined node renaming process, is guaranteed to contain as a subgraph the graph corresponding to target mesh M so long as d.gtoreq.2 and n.sub.d .gtoreq.3.