Triadic Closure — How Social Networks Cluster

Real social networks are not random: if two people share a mutual friend, they are far more likely to eventually connect with each other than two strangers are. This simulator grows a 3D social graph one node at a time using the Holme–Kim triadic-closure model — each arriving node attaches to the network with a first random link, then with tunable probability p either closes a friend-of-a-friend triangle or attaches randomly again. A force-directed layout keeps the live graph readable in 3D while the average local clustering coefficient is computed exactly every step and compared against the clustering expected of an equivalent random (Erdős–Rényi) graph, making visible — in real time — the mechanism that turns a random contact process into the tightly-knit communities seen in real friendship and collaboration networks.