Types of models used in the study of Percolation, and Percolation theory

Site percolation

Remove nodes (each with a given probability; or a fixed fraction. These are the same in the limit of infinte $N$). Can have

• "Random attack". Remove random nodes.
• "Targeted attack". Remove nodes preferentially by degree, or by other metric. For an application of targeted attacks to the problem of influence maximization see Influence maximization in complex networks.

Bond percolation

Remove edges

K-core percolation

Prunning process for obtaining K-core of a network: one removes all nodes with fewer than K neighbours, and repeats this process

Explosive percolation

Percolation processes that show a discontinuous, or at least very steep phase transition.

• Achlioptas process
• Half-restricted process
• Spanning cluster-avoiding (SCA) process

Bootstrap percolation

http://research.microsoft.com/en-us/um/people/holroyd/boot/

An "infection" process in which nodes become infected if sufficiently many of their neighbors are infected. Related to the Centola-Many threshold model for social contagions.

Limited path percolation

One construes "connectivity" as implying that a sufficiently short path still exists after some network components have been removed. To appreciate this idea, imagine trying to navigate a city in which some streets are blocked.

K-clique percolation

Percolation of K-cliques (completely connected subgraphs of K nodes) has been used to study the algorithmic detection of dense sets of nodes known as "communities" (see Uncovering the overlapping community structure of complex networks in nature and society pdf).

Percolation in Multilayer networks

• Percolation in Multiplex networks
• Percolation in interdependent networks

Non-self-averaging percolation process

A type of process that is non-self-averaging, in the sense that the relative variance of the size of the largest component doesn't vanish in the thermodynamic limit.

• Fractional percolation

Correlated percolation

Directed percolation

Percolation on a directed Network.

Other

• Invasive percolation
• Quorum percolation, and neuropercolation
• jamming percolation. showing a combination of first-order and second-order transition properties.
• First-passage percolation
• Multi-percolation