### Abstract

This paper attempts to provide viral marketeers guidance in terms of an investment level that could help capture some desired γ percentage of the market-share by some target time t with a desired level of confidence. To do this, we first introduce a diffusion model for social networks. A distance-dependent random graph is then considered as a model for the underlying social network, which we use to analyze the proposed diffusion model. Using the fact that vertices degrees have an almost Poisson distribution in distance-dependent random networks, we then provide a lower bound on the probability of the event that the time it takes for an idea (or a product, disease, etc.) to dominate a pre-specified γ percentage of a social network (denoted by Rγ) is smaller than some pre-selected target time t > 0, i.e., we find a lower bound on the probability of the event {Rγ ≤ t}. Simulation results performed over a wide variety of networks, including random as well as real-world, are then provided to verify that our bound indeed holds in practice. The Kullback-Leibler divergence measure is used to evaluate performance of our lower bound over these groups of networks, and as expected, we note that for networks that deviate more from the Poisson degree distribution, our lower bound does worse.

Original language | English (US) |
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Title of host publication | Proceedings of the 2019 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, ASONAM 2019 |

Editors | Francesca Spezzano, Wei Chen, Xiaokui Xiao |

Publisher | Association for Computing Machinery, Inc |

Pages | 95-100 |

Number of pages | 6 |

ISBN (Electronic) | 9781450368681 |

DOIs | |

State | Published - Aug 27 2019 |

Event | 11th IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, ASONAM 2019 - Vancouver, Canada Duration: Aug 27 2019 → Aug 30 2019 |

### Publication series

Name | Proceedings of the 2019 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, ASONAM 2019 |
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### Conference

Conference | 11th IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, ASONAM 2019 |
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Country | Canada |

City | Vancouver |

Period | 8/27/19 → 8/30/19 |

### Keywords

- Diffusion models
- Influence maximization
- Random graph models
- Social networks
- Viral marketing

### ASJC Scopus subject areas

- Communication
- Computer Networks and Communications
- Information Systems and Management
- Sociology and Political Science

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## Cite this

*Proceedings of the 2019 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, ASONAM 2019*(pp. 95-100). (Proceedings of the 2019 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining, ASONAM 2019). Association for Computing Machinery, Inc. https://doi.org/10.1145/3341161.3342922