Final answer:
The double torus topology's diameter varies with network size, being k - 1 for odd k, and k for even k, conceptualized through its two interconnected donut-like grids.
Step-by-step explanation:
When considering a double torus topology with a network size of k x k, the network's diameter will depend on whether k is odd or even. To conceptualize this, envision a two-dimensional grid that wraps around both horizontally and vertically to create a donut-like structure, however, this structure is represented twice (thus double torus), and they are interconnected.
For an odd-sized network, the maximum distance between two points is ½(k - 1) in each grid of the double torus. Combining the two grids, the diameter is k - 1. Conversely, in an even-sized network, the farthest distance in each grid is k/2. When both grids are accounted for, the diameter would be k.
Visualizing this concept without an actual diagram can be challenging, but one can think of the grid as cells where moving from one cell to an adjacent cell constitutes a single step. The diameter of the network represents the maximum number of steps needed to travel between two furthest points in the network.