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The edge-averaging process on graphs with random initial opinions

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Analysis demonstrates fast convergence of opinion averages in graphs with random initial conditions, suggesting efficient applications in networks.

The edge-averaging process accelerates opinion consensus, especially with disordered initial opinions.
Convergence occurs much faster in random opinion settings, typically reaching consensus in polynomial time.
On infinite graphs, opinions converge to the mean, provided the initial values meet specific distribution criteria.
Understanding this process may enhance strategies in sensor and social networks for effective opinion estimation.

Elboim et al. (2025) studied this question.

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Analysis demonstrates fast convergence of opinion averages in graphs with random initial conditions, suggesting efficient applications in networks.