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Erschienen in:
2022 | OriginalPaper | Buchkapitel
Surprising Behavior of the Average Degree for a Node’s Neighbors in Growth Networks
verfasst von : Sergei Sidorov, Sergei Mironov, Sergei Tyshkevich
Erschienen in: Complex Networks & Their Applications X
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Abstract
We study the variation of the stochastic process that describes the temporal behavior of the average degree of the neighbors for a fixed node in the Barabási-Albert networks. It was previously known that the expected value of this random quantity grows logarithmically with the number of iterations. In this paper, we use the mean-field approach to derive difference stochastic equations, as well as their corresponding approximate differential equations, in order to find the dynamics of its variation in time. The noteworthy fact proved in this paper is that the variation of this process is bounded by a constant. This behavior is fundamentally different from the dynamics of variation in most known stochastic processes (e.g., the Wiener process), in which its value tends to infinity over time.