Hypercube internetwork topology

Hypercube networks consist of 2m nodes, which form the vertices of squares to create an internetwork connection.

A hypercube is basically a multidimensional mesh network with two nodes in each dimension.

Due to similarity, such topologies are usually grouped into a k-ary d-dimensional mesh topology family, where d represents the number of dimensions and k represents the number of nodes in each dimension.

[1] Hypercube interconnection network is formed by connecting N nodes that can be expressed as a power of 2.

The network is constructed by connecting the nodes that just differ by one bit in their binary representation.

The corners of the respective one-bit changed MSBs are connected to create the higher hypercube network.

The distance between two nodes in the network can be given by Hamming weight of (number of ones in) the XOR-operation between their respective binary labels.

This is commonly referred to as Deterministic, Dimension Ordered Routing model.

E-Cube routing works by traversing the network in the kth dimension where k is the least significant non-zero bit in the result of calculating distance.

In case of a hypercube the degree is m. This defines the maximum number of nodes that a message must pass through on its way from the source to the destination.

This is the lowest number of wires that you should cut in order to divide the network into two equal halves.