Based on Launchpad traffic and mailing list responses, Gabor and Tamas will soon be releasing igraph 0.6.  In celebration, I’ll be publishing a number of helpful lists and tables I’ve put together to organize information about igraph.

  In this post, we’ll cover the community detection algorithms (~i.e., clustering, partitioning, segmenting) available in 0.6 and their characteristics, such as their worst-case runtime performance and whether they support directed or weighted edges.  Much of the information below is gleaned from the igraph C documentation, source algorithm publications, and three years of tracking the 0.6 trunk.

Optimal Modularity

  In my mind, modularity is  more of a framework than just a simple function over a graph.  I don’t know how Mark feels, but the amount of work based on this idea, implicitly (~87,000) or explicitly (~1000), is staggering given the short six years since.

  That said, modularity is just a framework, and, like all frameworks, has its shortcomings.  If you are going to talk about modularity in a quantitative way, there are two must-read ideas on the topic:

• The performance of modularity maximization in practical contexts.
  B. H. Good, Y.-A. de Montjoye and A. Clauset.
  Physical Review E 81, 046106 (2010).
• Resolution limit in community detection
  Santo Fortunato, Marc Barthelemy
• More work on tradeoffs in this limit by Fortunato:
  Limits of modularity maximization in community detection
  Andrea Lancichinetti, Santo Fortunato

  TL;DR: The plateau of the  modularity surface we care about most behaves poorly in real networks, and, depending on |V| and |E| in absolute and relative terms, we might not see “smaller” clusters.

If you’re still going to calculate the optimal modularity configuration, here are the details:

• New to version 0.6: TRUE
• Directed edges: FALSE
• Weighted edges: FALSE
• Handles multiple components: TRUE
• Runtime: B^(|V|^2)

Edge-Betweenness

OK, time to get less verbose.  I’ll stick to the primary reference and igraph characteristics going forward:

• Community structure in social and biological networks
  M. Girvan and M. E. J. Newman
• New to version 0.6: FALSE
• Directed edges: TRUE
• Weighted edges: TRUE
• Handles multiple components: TRUE
• Runtime: |V||E|^2

Leading Eigenvector

• Finding community structure in networks using the eigenvectors of matrices
  MEJ Newman
  Phys Rev E 74:036104 (2006)
• New to version 0.6: FALSE
• Directed edges: FALSE
• Weighted edges: FALSE
• Handles multiple components: TRUE
• Runtime: c|V|^2 + |E|

Fast-Greedy

• Finding community structure in very large networks
  Aaron Clauset, M. E. J. Newman, Cristopher Moore
• Finding Community Structure in Mega-scale Social Networks
  Ken Wakita, Toshiyuki Tsurumi
• New to version 0.6: FALSE
• Directed edges: FALSE
• Weighted edges: TRUE
• Handles multiple components: TRUE
• Runtime: |V||E| log |V|

Multi-Level

• Fast unfolding of communities in large networks
  Vincent D. Blondel, Jean-Loup Guillaume, Renaud Lambiotte, Etienne Lefebvre
• New to version 0.6: TRUE
• Directed edges: FALSE
• Weighted edges: TRUE
• Handles multiple components: TRUE
• Runtime: “linear” when |V| \approx |E|; (a quick glance at the algorithm suggests this would be quadratic for fully-connected graphs)

Walktrap

• Computing communities in large networks using random walks
  Pascal Pons, Matthieu Latapy
• New to version 0.6: FALSE
• Directed edges: FALSE
• Weighted edges: TRUE
• Handles multiple components: FALSE
• Runtime: |E||V|^2

Label Propagation

• Near linear time algorithm to detect community structures in large-scale networks.
  Raghavan, U.N. and Albert, R. and Kumara, S.
  Phys Rev E 76, 036106. (2007)
• New to version 0.6: TRUE
• Directed edges: FALSE
• Weighted edges: TRUE
• Handles multiple components: FALSE
• Runtime: |V| + |E|

InfoMAP

• The map equation
  M. Rosvall, D. Axelsson, C. T. Bergstrom
• New to version 0.6: TRUE
• Directed edges: TRUE
• Weighted edges: TRUE
• Weighted nodes: TRUE
• Handles multiple components: FALSE
• Runtime: none given; looks worst case like |V|(|V| + |E|) based on quick reading.