### Abstract

Truss decomposition is a method used to analyze large sparse graphs in order to identify successively better connected subgraphs. Since in many domains the underlying graph changes over time, its associated truss decomposition needs to be updated as well. This work focuses on the problem of incrementally updating an existing truss decomposition and makes the following three significant contributions. First, it presents a theory that identifies how the truss decomposition can change as new edges get added. Second, it develops an efficient incremental algorithm that incorporates various optimizations to update the truss decomposition after every edge addition. These optimizations are designed to reduce the number of edges that are explored by the algorithm. Third, it extends this algorithm to batch updates (i.e., where the truss decomposition needs to be updated after a set of edges are added), which reduces the overall computations that need to be performed. We evaluated the performance of our algorithms on real-world datasets. Our incremental algorithm achieves over 250000x average speedup for inserting an edge in a graph with 10 million edges relative to the non-incremental algorithm. Further, our experiments on batch updates show that our batch algorithm consistently performs better than the incremental algorithm.

Original language | English (US) |
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Title of host publication | Proceedings - 2019 1st International Conference on Graph Computing, GC 2019 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 51-59 |

Number of pages | 9 |

ISBN (Electronic) | 9781728141299 |

DOIs | |

State | Published - Sep 2019 |

Event | 1st International Conference on Graph Computing, GC 2019 - Laguna Hills, United States Duration: Sep 25 2019 → Sep 27 2019 |

### Publication series

Name | Proceedings - 2019 1st International Conference on Graph Computing, GC 2019 |
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### Conference

Conference | 1st International Conference on Graph Computing, GC 2019 |
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Country | United States |

City | Laguna Hills |

Period | 9/25/19 → 9/27/19 |

### Keywords

- batch graph algorithms
- network science
- streaming graph algorithms
- truss
- truss decomposition

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## Cite this

*Proceedings - 2019 1st International Conference on Graph Computing, GC 2019*(pp. 51-59). [9030981] (Proceedings - 2019 1st International Conference on Graph Computing, GC 2019). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/GC46384.2019.00016