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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.

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