Natural Emergence of Clusters

based on J. Bagrow & D. Brockmann, Natural emergence of clusters and bursts in network evolution, Phys. Rev. X, 3 021016 (2013)
The simulation below illustrates a network growth process in which incoming nodes attach their links preferentially to existing nodes that have a high clustering coefficient. The clustering coefficient quantifies how much a node’s neighbors are connected among each other. When all neighbors of an existing node are connected, the clustering coefficient is highest. When a node’s neighbors are not connected the coefficient is smallest. When nodes are added to the network they are thus attracted to regions of high internal connectivity. After they attach, they dilute this connectivity, making the region of the network less attractive for the next nodes. By this mechanism clusters emerge naturally.

The color from dark red to white quantifies the age of a node, the size of the nodes their degree (number of neighbors).