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Message-Passing Methods for Complex Contagions
- Publication Year :
- 2017
-
Abstract
- Message-passing methods provide a powerful approach for calculating the expected size of cascades either on random networks (e.g., drawn from a configuration-model ensemble or its generalizations) asymptotically as the number $N$ of nodes becomes infinite or on specific finite-size networks. We review the message-passing approach and show how to derive it for configuration-model networks using the methods of (Dhar et al., 1997) and (Gleeson, 2008). Using this approach, we explain for such networks how to determine an analytical expression for a "cascade condition", which determines whether a global cascade will occur. We extend this approach to the message-passing methods for specific finite-size networks (Shrestha and Moore, 2014; Lokhov et al., 2015), and we derive a generalized cascade condition. Throughout this chapter, we illustrate these ideas using the Watts threshold model.<br />Comment: 14 pages, 3 figures
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1703.08046
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/978-3-319-77332-2_5