In a high performance supercomputer, nodes (eg. 143A) are connected via extended diagonal links (142) in addition to the wraparound links which connect eg. node 3,1 to node 3, 6 and provide a toroidal topology. x 1 and x 2 are Cartesian directions such that Wx 1 and Wx 2 are differences in position from a given node (ie. number of 'hops'), and so nearest-neighbour links are 'Cartesian' links for which Wx =1. Other links may be 'iso-delta' diagonal links such that Wx 1 = Wx 2 =...= Wx D where the subscript denotes the dimensionality of the toroid (eg. for a 2 dimensional toroid Wx =2 or more), and the maximum latency n (ie. greatest number of 'hops' between two nodes) is such that Wx 1..D = n/2. These extended diagonal links reduce latency uniformly in different directions and increase the minimum bi-section bandwidth of a toroid, thus achieving desirable characteristics of both 'fat tree' (fig. 4) and toroid (figs. 7 and 8) network topologies.
Network topology having nodes interconnected by extended diagonal links