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- W2963586314 abstract "Let w:[0,1]2→[0,1] be a symmetric function, and consider the random process G(n,w), where vertices are chosen from [0,1] uniformly at random, and w governs the edge formation probability. Such a random graph is said to have a linear embedding, if the probability of linking to a particular vertex v decreases with distance. The rate of decrease, in general, depends on the particular vertex v. A linear embedding is called uniform if the probability of a link between two vertices depends only on the distance between them. In this article, we consider the question whether it is possible to “transform” a linear embedding to a uniform one, through replacing the uniform probability space [0,1] with a suitable probability space on R. We give necessary and sufficient conditions for the existence of a uniform linear embedding for random graphs where w attains only a finite number of values. Our findings show that for a general w the answer is negative in most cases." @default.
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- W2963586314 date "2017-03-01" @default.
- W2963586314 modified "2023-10-18" @default.
- W2963586314 title "Uniform linear embeddings of graphons" @default.
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- W2963586314 doi "https://doi.org/10.1016/j.ejc.2016.09.004" @default.
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