Kleinberg's Small-World model

Kleinberg's Small-World model describes how networks like social connections or the internet are structured. It proposes that most links are short-distance, connecting nearby nodes, but some links stretch across long distances, creating shortcuts. These long connections follow a specific probability: the farther apart two nodes are, the less likely they are connected, with the chance decreasing proportionally to the distance raised to a power. This balance of local and long-range links makes the network efficient for navigating quickly between any two points, mimicking real-world small-world phenomena like social circles and information spread.