Bond percolation

Bond percolation studies how connections form in a network when each link between nodes (points) is randomly open or closed. Imagine a grid where each connection can be active with some probability. As more connections open, clusters of interconnected nodes grow. When enough bonds are open, a large-scale path spans the entire system, allowing flow or communication across it. This transition point—called the percolation threshold—marks the shift from small, isolated clusters to a giant connected component. Bond percolation models are useful for understanding phenomena like fluid flow through porous materials or the robustness of networks.