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https://github.com/puzzlef/louvain-communities-dynamic

Comparing static vs dynamic approaches of the Louvain algorithm for community detection.
https://github.com/puzzlef/louvain-communities-dynamic

aggregation algorithm community detection experiment graph iterative local louvain moving

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Comparing static vs dynamic approaches of the Louvain algorithm for community detection.

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Comparing *static* vs *dynamic* approaches of the [Louvain algorithm] for

[community detection].



[Louvain] is an algorithm for **detecting communities in graphs**. *Community*

*detection* helps us understand the *natural divisions in a network* in an

**unsupervised manner**. It is used in **e-commerce** for *customer*

*segmentation* and *advertising*, in **communication networks** for *multicast*

*routing* and setting up of *mobile networks*, and in **healthcare** for

*epidemic causality*, setting up *health programmes*, and *fraud detection* is

hospitals. *Community detection* is an **NP-hard** problem, but heuristics exist

to solve it (such as this). **Louvain algorithm** is an **agglomerative-hierarchical**

community detection method that **greedily optimizes** for **modularity**

(**iteratively**).



**Modularity** is a score that measures *relative density of edges inside* vs

*outside* communities. Its value lies between `−0.5` (*non-modular clustering*)

and `1.0` (*fully modular clustering*). Optimizing for modularity *theoretically*

results in the best possible grouping of nodes in a graph.



Given an *undirected weighted graph*, all vertices are first considered to be

*their own communities*. In the **first phase**, each vertex greedily decides to

move to the community of one of its neighbors which gives greatest increase in

modularity. If moving to no neighbor's community leads to an increase in

modularity, the vertex chooses to stay with its own community. This is done

sequentially for all the vertices. If the total change in modularity is more

than a certain threshold, this phase is repeated. Once this **local-moving**

**phase** is complete, all vertices have formed their first hierarchy of

communities. The **next phase** is called the **aggregation phase**, where all

the *vertices belonging to a community* are *collapsed* into a single

**super-vertex**, such that edges between communities are represented as edges

between respective super-vertices (edge weights are combined), and edges within

each community are represented as self-loops in respective super-vertices

(again, edge weights are combined). Together, the local-moving and the

aggregation phases constitute a **pass**. This super-vertex graph is then used

as input for the next pass. This process continues until the increase in

modularity is below a certain threshold. As a result from each pass, we have a

*hierarchy of community memberships* for each vertex as a **dendrogram**. We

generally consider the *top-level hierarchy* as the *final result* of community

detection process.



*Louvain* algorithm is a hierarchical algorithm, and thus has two different

tolerance parameters: `tolerance` and `passTolerance`. **tolerance** defines the

minimum amount of increase in modularity expected, until the local-moving phase

of the algorithm is considered to have converged. We compare the increase in

modularity in each iteration of the local-moving phase to see if it is below

`tolerance`. **passTolerance** defines the minimum amount of increase in

modularity expected, until the entire algorithm is considered to have converged.

We compare the increase in modularity across all iterations of the local-moving

phase in the current pass to see if it is below `passTolerance`. `passTolerance`

is normally set to `0` (we want to maximize our modularity gain), but the same

thing does not apply for `tolerance`. Adjusting values of `tolerance` between

each pass have been observed to impact the runtime of the algorithm, without

significantly affecting the modularity of obtained communities. In this

experiment, we compare the performance of *three different types* of **dynamic**

**Louvain** with respect to the *static* version.



**Naive dynamic**:

- We start with previous community membership of each vertex (instead of each vertex its own community).



**Delta screening**:

- All edge batches are undirected, and sorted by source vertex-id.

- For edge additions across communities with source vertex `i` and highest modularity changing edge vertex `j*`,

  `i`'s neighbors and `j*`'s community is marked as affected.

- For edge deletions within the same community `i` and `j`,

  `i`'s neighbors and `j`'s community is marked as affected.



**Frontier-based**:

- All source and destination vertices are marked as affected for insertions and deletions.

- For edge additions across communities with source vertex `i` and destination vertex `j`,

  `i` is marked as affected.

- For edge deletions within the same community `i` and `j`,

  `i` is marked as affected.

- Vertices whose communities change in local-moving phase have their neighbors marked as affected.



The input data used for the experiments is available from the

[SuiteSparse Matrix Collection]. These experiments are done with guidance

from [Prof. Kishore Kothapalli] and [Prof. Dip Sankar Banerjee].







### Comparing various Naive-dynamic approaches



In this experiment ([approaches-naive]), we compare the performance of *two*

*different types* of **naive dynamic Louvain** with respect to the *static*

version. The **last** approach (`louvainSeqDynamicLast`) considers the community

membership of each vertex *after* the Louvain algorithm has *converged*

(community membership from the "last" pass) and then performs the Louvain

algorithm upon the new (updated) graph. This is *similar* to naive dynamic

approaches with other algorithms. On the other hand, the **first** approach

(`louvainSeqDynamicFirst`) considers the community membership of each vertex

right after the *first pass* of the Louvain algorithm (this is the first

community membership hierarchy) and then performs the Louvain algorithm upon the

updated graph. With this approach, we allow the affected vertices to choose

their community membership from the first pass itself, which which to my

intuition would lead to better communities.



First, we compute the community membership of each vertex using the static

Louvain algorithm (`louvainSeqLast`). We also run the static Louvain algorithm

for only one pass (`louvainSeqFirst`). We then generate *batches* of *insertions*

*(+)* and *deletions (-)* of edges of sizes 500, 1000, 5000, ... 100000. For each

batch size, we generate *five* different batches for the purpose of *averaging*.

Each batch of edges (insertion / deletion) is generated randomly such that the

selection of each vertex (as endpoint) is *equally probable*. We choose the

Louvain *parameters* as `resolution = 1.0`, `tolerance = 1e-2` (for local-moving

phase) with *tolerance* decreasing after every pass by a factor of

`toleranceDeclineFactor = 10`, and a `passTolerance = 0.0` (when passes stop).

In addition we limit the maximum number of iterations in a single local-moving

phase with `maxIterations = 500`, and limit the maximum number of passes with

`maxPasses = 500`. We run the Louvain algorithm until convergence (or until the

maximum limits are exceeded), and measure the **time** **taken** for the

*computation* (performed 5 times for averaging), the **modularity score**, the

**total number of iterations** (in the *local-moving* *phase*), and the number

of **passes**. This is repeated for *seventeen* different graphs.



From the results, we make make the following observations. The performance of

dynamic approaches upon a batch of deletions appears to *increase* with *increasing*

batch size*. This makes sense since, as the graph keeps getting smaller, the

computation would complete *sooner*. Next, the `first` naive dynamic approach is

found to be *significantly slower* (~0.3x speedup) than the `last` approach.

However, the `first` approach is *still faster* than the static approach upto a

batch size of `50000`. On the other hand, the `last` approach is *faster* than the

static approach for all batch sizes. A similar behavior is observed with the

total number of iterations. The `first` approach seems to have a *slightly higher*

modularity with respect to the `last` approach. Since the modularity between the

two dynamic approaches are almost the same, the **last** approach is clearly the

**best choice**.



[approaches-naive]: https://github.com/puzzlef/louvain-communities-dynamic/tree/approaches-naive







### Comparision with Static approach



First ([compare-static], [main]), we compute the community membership of each vertex

using the static Louvain algorithm. We then generate *batches* of *insertions*

*(+)* and *deletions (-)* of edges of sizes 500, 1000, 5000, ... 100000. For

each batch size, we generate *five* different batches for the purpose of

*averaging*. Each batch of edges (insertion / deletion) is generated randomly

such that the selection of each vertex (as endpoint) is *equally probable*. We

choose the Louvain *parameters* as `resolution = 1.0`, `tolerance = 1e-2` (for

local-moving phase) with *tolerance* decreasing after every pass by a factor of

`toleranceDeclineFactor = 10`, and a `passTolerance = 0.0` (when passes stop).

In addition we limit the maximum number of iterations in a single local-moving

phase with `maxIterations = 500`, and limit the maximum number of passes with

`maxPasses = 500`. We run the Louvain algorithm until convergence (or until the

maximum limits are exceeded), and measure the **time taken** for the

*computation* (performed 5 times for averaging), the **modularity score**, the

**total number of iterations** (in the *local-moving* *phase*), and the number

of **passes**. This is repeated for *seventeen* different graphs.



From the results, we make make the following observations. The frontier-based

dynamic approach converges the fastest, which obtaining communities with only

slightly lower modularity than other approaches. We also observe that

delta-screening based dynamic Louvain algorithm has the same performance as that

of the naive dynamic approach. Therefore, **frontier-based dynamic Louvain**

would be the **best choice**. All outputs are saved in a [gist]. Some [charts]

are also included below, generated from [sheets].



[![](https://i.imgur.com/MVFks1a.png)][sheetp]

[![](https://i.imgur.com/du5qe69.png)][sheetp]

[![](https://i.imgur.com/AulWzoj.png)][sheetp]

[![](https://i.imgur.com/bxpYvsF.png)][sheetp]



[compare-static]: https://github.com/puzzlef/louvain-communities-dynamic/tree/compare-static

[main]: https://github.com/puzzlef/louvain-communities-dynamic














## References



- [Fast unfolding of communities in large networks; Vincent D. Blondel et al. (2008)](https://arxiv.org/abs/0803.0476)

- [Community Detection on the GPU; Md. Naim et al. (2017)](https://arxiv.org/abs/1305.2006)

- [Scalable Static and Dynamic Community Detection Using Grappolo; Mahantesh Halappanavar et al. (2017)](https://ieeexplore.ieee.org/document/8091047)

- [From Louvain to Leiden: guaranteeing well-connected communities; V.A. Traag et al. (2019)](https://www.nature.com/articles/s41598-019-41695-z)

- [Community detection in networks: A multidisciplinary review; Muhammad Aqib Javed et al. (2018)](https://www.sciencedirect.com/science/article/abs/pii/S1084804518300560)

- [Adaptive parallel Louvain community detection on a multicore platform; Mahmood Fazlali et al. (2017)](https://www.sciencedirect.com/science/article/abs/pii/S014193311630240X)

- [A signal processing perspective to community detection in dynamic networks; Selin Aviyente (2021)](https://www.sciencedirect.com/science/article/abs/pii/S1051200421002311)

- [Incremental Community Detection in Distributed Dynamic Graph; Tariq Abughofa et al. (2021)](https://ieeexplore.ieee.org/abstract/document/9564329)

- [Community Detection in Dynamic Attributed Graphs; Gonzalo A. Bello et al. (2016)](https://link.springer.com/chapter/10.1007/978-3-319-49586-6_22)

- [Dynamic Community Detection Using Nonnegative Matrix Factorization; Feng Gao et al. (2017)](https://ieeexplore.ieee.org/abstract/document/8327706)

- [Improving fuzzy C-mean-based community detection in social networks using dynamic parallelism; Mahmoud Al-Ayyoub et al. (2019)](https://www.sciencedirect.com/science/article/abs/pii/S0045790617315641)

- [Distributed Louvain Algorithm for Graph Community Detection; Sayan Ghosh et al. (2018)](https://ieeexplore.ieee.org/abstract/document/8425242)

- [Evaluating community detection algorithms for progressively evolving graphs; Remy Cazabet et al. (2020)](https://academic.oup.com/comnet/article-abstract/8/6/cnaa027/6161494?login=false)

- [Scalable distributed Louvain algorithm for community detection in large graphs; Naw Safrin Sattar et al. (2022)](https://link.springer.com/article/10.1007/s11227-021-04224-2)

- [Community Detection in Evolving Networks; Tejas Puranik et al. (2017)](https://ieeexplore.ieee.org/abstract/document/9069125)

- [Incremental local community identification in dynamic social networks; Mansoureh Takaffoli et al. (2013)](https://ieeexplore.ieee.org/abstract/document/6785692)

- [Dynamic community detection based on the Matthew effect; Zejun Sun et al. (2022)](https://www.sciencedirect.com/science/article/abs/pii/S0378437122002564)

- [Community detection in social networks; Punam Bedi et al. (2016)](https://wires.onlinelibrary.wiley.com/doi/abs/10.1002/widm.1178)

- [Long range community detection; Thomas Aynaud et al. (2010)](https://inria.hal.science/inria-00531750/)

- [Dynamic Community Detection Algorithm Based on Incremental Identification; Xiaoming Li et al. (2015)](https://ieeexplore.ieee.org/abstract/document/7395763)

- [An Improved Louvain Algorithm for Community Detection; Jicun Zhang et al. (2021)](https://onlinelibrary.wiley.com/doi/10.1155/2021/1485592)

- [DyPerm: Maximizing Permanence for Dynamic Community Detection; Prerna Agarwal et al. (2018)](https://link.springer.com/chapter/10.1007/978-3-319-93034-3_35)

- [A fast and efficient incremental approach toward dynamic community detection; Neda Zarayeneh et al. (2019)](https://dl.acm.org/doi/abs/10.1145/3341161.3342877)

- [Scalable Community Detection with the Louvain Algorithm; Xinyu Que et al. (2015)](https://ieeexplore.ieee.org/abstract/document/7161493)

- [DynaMo: Dynamic Community Detection by Incrementally Maximizing Modularity; Di Zhuang et al. (2019)](https://ieeexplore.ieee.org/abstract/document/8890861)

- [C-Blondel: An Efficient Louvain-Based Dynamic Community Detection Algorithm; Mahsa Seifikar et al. (2020)](https://ieeexplore.ieee.org/abstract/document/8982190)

- [Scalable static and dynamic community detection using Grappolo; Mahantesh Halappanavar et al. (2017)](https://ieeexplore.ieee.org/abstract/document/8091047)

- [Dynamic community detection in evolving networks using locality modularity optimization; Mário Cordeiro et al. (2016)](https://link.springer.com/article/10.1007/s13278-016-0325-1)

- [A Dynamic Modularity Based Community Detection Algorithm for Large-scale Networks: DSLM; Riza Aktunc et al. (2015)](https://dl.acm.org/doi/abs/10.1145/2808797.2808822)

- [An Analysis of the Dynamic Community Detection Algorithms in Complex Networks; Dhananjay Kumar Singh et al. (2020)](https://ieeexplore.ieee.org/abstract/document/9067224)

- [Dynamic Community Detection Decouples Multiple Time Scale Behavior of Complex Chemical Systems; Neda Zarayeneh et al. (2022)](https://pubs.acs.org/doi/full/10.1021/acs.jctc.2c00454)

- [Targeted revision: A learning-based approach for incremental community detection in dynamic networks; Jiaxing Shang et al. (2016)](https://www.sciencedirect.com/science/article/abs/pii/S0378437115008080)

- [DynComm R Package -- Dynamic Community Detection for Evolving Networks; Rui Portocarrero Sarmento et al. (2019)](https://arxiv.org/abs/1905.01498)

- [CS224W: Machine Learning with Graphs | Louvain Algorithm; Jure Leskovec (2021)](https://www.youtube.com/watch?v=0zuiLBOIcsw)

- [The University of Florida Sparse Matrix Collection; Timothy A. Davis et al. (2011)](https://doi.org/10.1145/2049662.2049663)










[![](https://i.imgur.com/UGB0g2L.jpg)](https://www.youtube.com/watch?v=pIF3wOet-zw)


[![ORG](https://img.shields.io/badge/org-puzzlef-green?logo=Org)](https://puzzlef.github.io)

[![DOI](https://zenodo.org/badge/538336155.svg)](https://zenodo.org/badge/latestdoi/538336155)



[Prof. Dip Sankar Banerjee]: https://sites.google.com/site/dipsankarban/

[Prof. Kishore Kothapalli]: https://faculty.iiit.ac.in/~kkishore/

[SuiteSparse Matrix Collection]: https://sparse.tamu.edu

[Louvain algorithm]: https://en.wikipedia.org/wiki/Louvain_method

[community detection]: https://en.wikipedia.org/wiki/Community_search

[Louvain]: https://en.wikipedia.org/wiki/Louvain_method

[gist]: https://gist.github.com/wolfram77/de2c1e1c8f6efb7f4053a122b688c7a7

[charts]: https://imgur.com/a/xcoVmDw

[sheets]: https://docs.google.com/spreadsheets/d/1U8cdi0Y9i-Pl0SkUdSsuM87Khw0Jn6SCM7u6qlVp--Y/edit?usp=sharing

[sheetp]: https://docs.google.com/spreadsheets/d/e/2PACX-1vQjZGdwSy2Cd5mojCQgvvl0P5eaZBjJwhIBqcX-RN5MfeFVl9V2o9G4XCjR2_qaH_mpeBSm7eMIhSeQ/pubhtml