In the study of complex networks, one of the most challenging tasks is to construct mathematical models that are flexible enough to reproduce phenomena observed in the real world, yet simple enough to be both simulated and studied analytically. This paper develops a highly general model of random networks in which connections appear with arbitrary probabilities independently of each other. The calculation explores how the probability of the entire network being connected behaves as its total size grows. As observed in many cases studied in the scientific literature so far, this behavior depends on the properties of the most peripheral elements of the network.

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By Lorenzo Federico - the research was also conducted at the University of Warwick.