### Abstract

In this paper, we argue for representing networks as a bag of triangular motifs, particularly for important network problems that current model-based approaches handle poorly due to computational bottlenecks incurred by using edge representations. Such approaches require both 1-edges and 0-edges (missing edges) to be provided as input, and as a consequence, approximate inference algorithms for these models usually require Ω(N^{2}) time per iteration, precluding their application to larger real-world networks. In contrast, triangular modeling requires less computation, while providing equivalent or better inference quality. A triangular motif is a vertex triple containing 2 or 3 edges, and the number of such motifs is Θ(Σ _{i} D_{i}^{2}) (where D_{i} is the degree of vertex i), which is much smaller than N^{2} for low-maximum-degree networks. Using this representation, we develop a novel mixed-membership network model and approximate inference algorithm suitable for large networks with low max-degree. For networks with high maximum degree, the triangular motifs can be naturally subsampled in a node-centric fashion, allowing for much faster inference at a small cost in accuracy. Empirically, we demonstrate that our approach, when compared to that of an edge-based model, has faster runtime and improved accuracy for mixed-membership community detection. We conclude with a large-scale demonstration on an N ≈ 280, 000-node network, which is infeasible for network models with (N^{2}) inference cost.

Original language | English (US) |
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Title of host publication | Advances in Neural Information Processing Systems 25 |

Subtitle of host publication | 26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012 |

Pages | 2132-2140 |

Number of pages | 9 |

State | Published - Dec 1 2012 |

Externally published | Yes |

Event | 26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012 - Lake Tahoe, NV, United States Duration: Dec 3 2012 → Dec 6 2012 |

### Publication series

Name | Advances in Neural Information Processing Systems |
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Volume | 3 |

ISSN (Print) | 1049-5258 |

### Other

Other | 26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012 |
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Country | United States |

City | Lake Tahoe, NV |

Period | 12/3/12 → 12/6/12 |

### ASJC Scopus subject areas

- Computer Networks and Communications
- Information Systems
- Signal Processing

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## Cite this

*Advances in Neural Information Processing Systems 25: 26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012*(pp. 2132-2140). (Advances in Neural Information Processing Systems; Vol. 3).