Was ist die Small-World-Eigenschaft?

The small world property refers to a phenomenon observed in certain types of networks, where most nodes can be reached from every other node through a small number of steps, despite the network's large size. This concept is often illustrated by the "six degrees of separation" theory, which suggests that any two people in the world are connected through a chain of acquaintances that typically does not exceed six intermediaries.

In mathematical terms, a network exhibits the small world property if:

1. The average path length between nodes is relatively short compared to the total number of nodes in the network.
2. There is a high clustering coefficient, meaning that if two nodes are connected to a common node, they are likely to be connected to each other as well.

This property is significant in various fields, including sociology, epidemiology, and computer science, as it helps explain how information, diseases, or behaviors can spread rapidly through populations.