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We extend the work of Antunovi{c}, Mossel and R{a}cz on competing types in preferential attachment models to include cases where the types have different fitnesses, which may be either multiplicative or additive. We will show that, depending on the values of the parameters of the models, there are different possible limiting behaviours depending on the zeros of a certain function. In particular we will show the existence of choices of the parameters where one type is favoured both by having higher fitness and by the type attachment mechanism, but the other type has a positive probability of dominating the network in the limit.
We consider the preferential attachment model with multiple vertex types introduced by Antunovic, Mossel and Racz. We give an example with three types, based on the game of rock-paper-scissors, where the proportions of vertices of the different types
We introduce a new model of preferential attachment with fitness, and establish a time reversed duality between the model and a system of branching-coalescing particles. Using this duality, we give a clear and concise explanation for the condensation
Preferential attachment networks are a type of random network where new nodes are connected to existing ones at random, and are more likely to connect to those that already have many connections. We investigate further a family of models introduced b
We propose a random graph model with preferential attachment rule and emph{edge-step functions} that govern the growth rate of the vertex set. We study the effect of these functions on the empirical degree distribution of these random graphs. More sp
We consider the degree distributions of preferential attachment random graph models with choice similar to those considered in recent work by Malyshkin and Paquette and Krapivsky and Redner. In these models a new vertex chooses $r$ vertices according