Local Community Detection Based on Small Cliques
Abstract
:1. Introduction
1.1. Related Work
1.2. Preliminaries
2. Density-Based Local Community Detection Algorithms
2.1. GCE M/L
Implementation Details
2.2. Two-Phase L
- and
- and
- and
Implementation Details
2.3. LFM
Implementation Details
2.4. PageRank-Nibble
3. Local Community Detection Algorithms Based on Small Cliques
3.1. LTE
Implementation Details
3.2. Local T
Implementation Details
3.3. Clique Based Community Expansion
Implementation Details
3.4. Triangle Based Community Expansion
Algorithm 1: Triangle Based Community Expansion (TCE) detects a community around a given node. Uses a node scoring function based on triangles to add nodes to the community. |
|
Implementation Details
4. Experiments
4.1. Experimental Setup
4.2. Scoring
4.3. Synthetic Graphs
Unweighted Graphs
4.4. Overlapping Communities
Weighted Graphs
4.5. Facebook Graphs
4.6. Running Times
4.7. Summary
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Name | Description | Unweighted | Overlapping | Weighted |
---|---|---|---|---|
n | number of nodes | 5000 | 2000 | 5000 |
k | average degree | 20 | 39.5, 61.5, 78.1, 91.8, 103.5 | 20 |
maximum degree | 50 | 120 | 50 | |
degree exponent | ||||
minimum community size | 10, 20 | 60 | 20 | |
maximum community size | 50, 100 | 120 | 100 | |
community size exponent | ||||
topological mixing | 0.1, …, 0.9 | 0.2 | 0.3, 0.5, 0.8 | |
weight exponent | ||||
weight mixing | 0.1, …, 0.9 | |||
communities per node | 1 | 1, ..., 5 | 1 |
(a) On the Overlapping LFR Benchmark. | (b) On the 100 Facebook Networks. | ||||
---|---|---|---|---|---|
Size | Time (ms) | Size | Time (ms) | ||
Cl | 7 | 0.4 | TwoPhaseL | 38 | 1.7 |
Cl+PRN | 419 | 2.1 | PRN | 975 | 4.2 |
PRN | 605 | 2.9 | GCE M | 282 | 5.9 |
Cl+GCE M | 321 | 3.5 | GCE L | 270 | 6.7 |
GCE M | 405 | 3.7 | LFMLocal | 221 | 9.8 |
Cl+GCE L | 333 | 4.0 | TCE | 321 | 11.4 |
GCE L | 411 | 4.4 | Cl | 14 | 13.0 |
LFMLocal | 249 | 4.8 | Cl+TwoPhaseL | 52 | 17.5 |
Cl+LFM | 242 | 5.1 | Cl+PRN | 1086 | 18.5 |
Cl+TwoPhaseL | 243 | 5.3 | Cl+GCE M | 1009 | 45.1 |
TwoPhaseL | 329 | 6.8 | Cl+TCE | 930 | 46.5 |
TCE | 320 | 10.2 | Cl+GCE L | 919 | 48.0 |
Cl+TCE | 320 | 10.5 | Cl+LFM | 907 | 77.4 |
LTE | 294 | 26.4 | LTE | 257 | 107.5 |
Cl+LTE | 436 | 28.8 | Cl+LTE | 407 | 150.5 |
LocalT | 1618 | 49.7 | LocalT | 8066 | 1028.1 |
Cl+LocalT | 1589 | 49.7 | Cl+LocalT | 8207 | 1054.7 |
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Hamann, M.; Röhrs, E.; Wagner, D. Local Community Detection Based on Small Cliques. Algorithms 2017, 10, 90. https://doi.org/10.3390/a10030090
Hamann M, Röhrs E, Wagner D. Local Community Detection Based on Small Cliques. Algorithms. 2017; 10(3):90. https://doi.org/10.3390/a10030090
Chicago/Turabian StyleHamann, Michael, Eike Röhrs, and Dorothea Wagner. 2017. "Local Community Detection Based on Small Cliques" Algorithms 10, no. 3: 90. https://doi.org/10.3390/a10030090