  In complex network research clique percolation, introduced by Palla et al.,
is a deterministic community detection method, which allows for overlapping
communities and is purely based on local topological properties of a network.
Here we present a sequential clique percolation algorithm (SCP) to do fast
community detection in weighted and unweighted networks, for cliques of a
chosen size. This method is based on sequentially inserting the constituent
links to the network and simultaneously keeping track of the emerging community
structure. Unlike existing algorithms, the SCP method allows for detecting
k-clique communities at multiple weight thresholds in a single run, and can
simultaneously produce a dendrogram representation of hierarchical community
structure. In sparse weighted networks, the SCP algorithm can also be used for
implementing the weighted clique percolation method recently introduced by
Farkas et al. The computational time of the SCP algorithm scales linearly with
the number of k-cliques in the network. As an example, the method is applied to
a product association network, revealing its nested community structure.
