This explorable illustrates how strong heterogeneities, cluster-like structures and high variability in node connectivities can naturally emerge in growing networks. The mechanism explored here is very simple: When a new node is added to the network it picks another target node at random. Instead of linking to it, the new node establishes a link to one of the target’s neighbors.

This explorable illustrates a dynamic network model that was designed to capture the emergence of community structures, heterogeneities and clusters that are frequently observed in social networks. Clusters are characterized by a high probability that a person’s ‘friends are also friends’. In this model not only the connectivity evolves but also the strength of links between nodes. The model was orginally proposed by Jussi Kumpula, Jukka-Pekka Onnela, Jari Saramäki, János Kertész and Kimmo Kaski.

This explorable illustrates and compares three vaccination strategies in complex networks. In this type of model nodes are people and network links potential transmission paths. “Vaccination” then means that nodes are disconnected from the network because they can no longer acquire or transmit a disease. Vaccination thus effectively dilutes the network. Two strategies, A and B, are straightforward to understand. A third one, C, is a bit odd and counterintuitive at first glance:

This explorable illustrates an important feature of complex networks: the emergence of the giant component. Networks often have multiple components. A component is a part of the network where we can find a path between any two nodes by traversing links.

This explorable illustrates the mechanism of herd immunity. When an infectious disease spreads in a population, an individual can be protected by a vaccine that delivers immunity. But there’s a greater good. Immunization not only projects the individual directly. The immunized person will also never transmit the disease to others, effectively reducing the likelihood that the disease can proliferate in the population. Because of this, a disease can be eradicated even if not the entire population is immunized. This population wide effect is known as herd immunity.

This explorable illustrates a network model that captures how opinion dynamics might work in a population and how clusters of uniform opinion might naturally emerge from an initially random system. The model is a variant of a model introduced by P. Holme and M. Newman in a 2006 paper: Nonequilibrium phase transition in the coevolution of networks and opinions.

This explorable illustrates network growth based on preferential attachment, a variant of the Barabasi-Albert model that was introduced to capture strong heterogeneities observed in many natural and technological networks. It has become a popular model for scale-free networks in nature.

Preferential attachment means that nodes that enter the network during a growth process preferentially connect to nodes with specific properties. In the original system, they preferentially connect to existing nodes that are already well connected, increasing their connectivity even further. This rich get richer effect generates networks in which a few nodes are very strongly connected and very many nodes poorly.