MCL (Markov Cluster Algorithm)

MCL (Markov Cluster Algorithm)

Markov Cluster Algorithm works by simulating a stochastic (Markov) flow in a weighted graph, where each node is a data point, and the edge weights are defined by the adjacency matrix. ... When the algorithm converges, it produces the new edge weights that define the new connected components of the graph (i.e. the clusters).

mcl(adj::AbstractMatrix; [kwargs...]) -> MCLResult

Perform MCL (Markov Cluster Algorithm) clustering using $n×n$ adjacency (points similarity) matrix adj.


Keyword arguments to control the MCL algorithm:

  • add_loops::Bool (enabled by default): whether the edges of weight 1.0 from the node to itself should be appended to the graph
  • expansion::Number (defaults to 2): MCL expansion constant
  • inflation::Number (defaults to 2): MCL inflation constant
  • save_final_matrix::Bool (disabled by default): whether to save the final equilibrium state in the mcl_adj field of the result; could provide useful diagnostic if the method doesn't converge
  • prune_tol::Number: pruning threshold
  • display, maxiter, tol: see common options


Stijn van Dongen, "Graph clustering by flow simulation", 2001

Original MCL implementation.

MCLResult <: ClusteringResult

The output of mcl function.


  • mcl_adj::AbstractMatrix: the final MCL adjacency matrix (equilibrium state matrix if the algorithm converged), empty if save_final_matrix option is disabled
  • assignments::Vector{Int}: indices of the points clusters. assignments[i] is the index of the cluster for the $i$-th point ($0$ if unassigned)
  • counts::Vector{Int}: the $k$-length vector of cluster sizes
  • nunassigned::Int: the number of standalone points not assigned to any cluster
  • iterations::Int: the number of elapsed iterations
  • rel_Δ::Float64: the final relative Δ
  • converged::Bool: whether the method converged