A simple model of global cascades on random hypergraphs
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arXiv
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911914990239744 |
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| author | Chen, Lei Zhu, Yanpeng Zhu, Jiadong Ruan, Zhongyuan Small, Michael Christensen, Kim Liu, Run-Ran Meng, Fanyuan |
| author_facet | Chen, Lei Zhu, Yanpeng Zhu, Jiadong Ruan, Zhongyuan Small, Michael Christensen, Kim Liu, Run-Ran Meng, Fanyuan |
| contents | This study introduces a comprehensive framework that situates information cascades within the domain of higher-order interactions, utilizing a double-threshold hypergraph model. We propose that individuals (nodes) gain awareness of information through each communication channel (hyperedge) once the number of information adopters surpasses a threshold $ϕ_m$. However, actual adoption of the information only occurs when the cumulative influence across all communication channels exceeds a second threshold, $ϕ_k$. We analytically derive the cascade condition for both the case of a single seed node using percolation methods and the case of any seed size employing mean-field approximation. Our findings underscore that when considering the fractional seed size, $r_0 \in (0,1]$, the connectivity pattern of the random hypergraph, characterized by the hyperdegree, $k$, and cardinality, $m$, distributions, exerts an asymmetric impact on the global cascade boundary. This asymmetry manifests in the observed differences in the boundaries of the global cascade within the $(ϕ_m, \langle m \rangle)$ and $(ϕ_k, \langle k \rangle)$ planes. However, as $r_0 \to 0$, this asymmetric effect gradually diminishes. Overall, by elucidating the mechanisms driving information cascades within a broader context of higher-order interactions, our research contributes to theoretical advancements in complex systems theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18850 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A simple model of global cascades on random hypergraphs Chen, Lei Zhu, Yanpeng Zhu, Jiadong Ruan, Zhongyuan Small, Michael Christensen, Kim Liu, Run-Ran Meng, Fanyuan Physics and Society This study introduces a comprehensive framework that situates information cascades within the domain of higher-order interactions, utilizing a double-threshold hypergraph model. We propose that individuals (nodes) gain awareness of information through each communication channel (hyperedge) once the number of information adopters surpasses a threshold $ϕ_m$. However, actual adoption of the information only occurs when the cumulative influence across all communication channels exceeds a second threshold, $ϕ_k$. We analytically derive the cascade condition for both the case of a single seed node using percolation methods and the case of any seed size employing mean-field approximation. Our findings underscore that when considering the fractional seed size, $r_0 \in (0,1]$, the connectivity pattern of the random hypergraph, characterized by the hyperdegree, $k$, and cardinality, $m$, distributions, exerts an asymmetric impact on the global cascade boundary. This asymmetry manifests in the observed differences in the boundaries of the global cascade within the $(ϕ_m, \langle m \rangle)$ and $(ϕ_k, \langle k \rangle)$ planes. However, as $r_0 \to 0$, this asymmetric effect gradually diminishes. Overall, by elucidating the mechanisms driving information cascades within a broader context of higher-order interactions, our research contributes to theoretical advancements in complex systems theory. |
| title | A simple model of global cascades on random hypergraphs |
| topic | Physics and Society |
| url | https://arxiv.org/abs/2402.18850 |