Self-Reinforced Preferential Attachment
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913961867214848 |
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| author | Dahiya, Yogesh Hollander, Frank den |
| author_facet | Dahiya, Yogesh Hollander, Frank den |
| contents | We consider a preferential attachment random graph with self-reinforcement. Each time a new vertex comes in, it attaches itself to an old vertex with a probability that is proportional to the sum of the degrees of that old vertex at all prior times. The resulting growing graph is a random tree whose vertices have degrees that grow polynomially fast in time. We compute the growth exponent, show that it is strictly larger than the growth exponent in the absence of self-reinforcement, and develop insight into how the self-reinforcement affects the growth. Proofs are based on a stochastic approximation scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_19322 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-Reinforced Preferential Attachment Dahiya, Yogesh Hollander, Frank den Probability 05C80, 60C05, 60F15 We consider a preferential attachment random graph with self-reinforcement. Each time a new vertex comes in, it attaches itself to an old vertex with a probability that is proportional to the sum of the degrees of that old vertex at all prior times. The resulting growing graph is a random tree whose vertices have degrees that grow polynomially fast in time. We compute the growth exponent, show that it is strictly larger than the growth exponent in the absence of self-reinforcement, and develop insight into how the self-reinforcement affects the growth. Proofs are based on a stochastic approximation scheme. |
| title | Self-Reinforced Preferential Attachment |
| topic | Probability 05C80, 60C05, 60F15 |
| url | https://arxiv.org/abs/2507.19322 |