Methods and systems for implementing a high radix network topology

Methods and systems related to construction and implementation of high radix topologies are disclosed. The nodes of the network topology are divided into a number of groups. Intra-group connections are constructed by connecting the nodes of each group according to a first complementary base graph. Inter-group connections are constructed based on a second complementary base graph and a plurality of permutation matrices. Each permutation matrix represents a pattern for selecting source group and destination group for each inter-group connection. One permutation matrix is randomly assigned to each edge of the second complementary base graph. An inter-group connection is constructed by identifying a source node and a destination node corresponding to a selected edge of the second complementary base graph, and identifying a source group and a destination group according to the permutation matrix assigned to the selected edge.