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We propose a scale-free network model with a tunable power-law exponent. ThePoisson growth model, as we call it, is an offshoot of the celebrated model ofBarab\'{a}si and Albert where a network is generated iteratively from a smallseed network; at each step a node is added together with a number of incidentedges preferentially attached to nodes already in the network. A key feature ofour model is that the number of edges added at each step is a random variablewith Poisson distribution, and, unlike the Barab\'{a}si-Albert model where thisquantity is fixed, it can generate any network. Our model is motivated by anapplication in Bayesian inference implemented as Markov chain Monte Carlo toestimate a network; for this purpose, we also give a formula for theprobability of a network under our model.

A preferential attachment model with Poisson growth for scale-free networks