But since this linearithmic function does not grow as rapidly as Metcalfe's law, it implies that many of the quantitative expectations based on Metcalfe's law were excessively optimistic.
The Mertens conjecture concerning its growth, conjecturing it bounded by x1/2, which would have implied the Riemann hypothesis, is now known to be false (Odlyzko and te Riele, 1985).
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Other analysts of network value functions, including Andrew Odlyzko and Eric S. Raymond, have argued that both Reed's Law and Metcalfe's Law overstate network value because they fail to account for the restrictive impact of human cognitive limits on network formation.