A glowing blue and purple transparent hypercube network structure with nodes and connecting lines, against a dark background filled with binary code.

The Hypercube Network (n-Cube) In computer science, a hypercube network is a highly efficient, parallel processing interconnection topology where the nodes (processors) and edges (communication links) map exactly to the vertices and edges of an n-dimensional hypercube. 1. Mathematical Theory (Geometry) \rightarrow Network Structure. The geometry of the hypercube dictates the topology of the network: * Dimensionality (n): A network with N processors is a hypercube of dimension n if N = 2^n. * Example: An 8-processor network is a 3D hypercube (8=2^3). A 16-processor network is a 4D hypercube or Tesseract (16=2^4). * Node Degree: In an n-dimensional hypercube, every node is connected to exactly n neighbors. * This is a highly advantageous property, as it guarantees that every processor has the same connectivity and workload. * Diameter (Maximum Distance): The maximum number of links (hops) required to send a message between any two nodes is \mathbf{n}. * This is the key advantage: as the number of processors N grows exponentially (2^n), the longest communication path (diameter) only grows linearly (n). For example, a system with 1,024 processors (n=10) has a maximum communication path of only 10 steps. 2. Number Systems (Real/Binary) \rightarrow Routing. The algebraic structure of the numbers used to define the hypercube geometry makes routing highly efficient. * Binary Labeling: Each processor (node) in an n-dimensional hypercube is assigned a unique n-bit binary address (its See more