Criticality and Popularity in Social Networks

Eberhard Mayerhofer

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arXiv · 2105.09359

Criticality and Popularity in Social Networks

Eberhard Mayerhofer

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Abstract

I find that several models for information sharing in social networks can be interpreted as age-dependent multi-type branching processes, and build them independently following Sewastjanow. This allows to characterize criticality in (real and random) social networks. For random networks, I develop a moment-closure method that handles the high-dimensionality of these models: By modifying the timing of sharing with followers, all users can be represented by a single representative, while leaving the total progeny unchanged. Thus I compute the exact popularity distribution, revealing a viral character of critical models expressed by fat tails of order minus three half.

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Eberhard Mayerhofer. 2021-05-19. Criticality and Popularity in Social Networks. https://arxiv.org/abs/2105.09359

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