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An important characteristic of flocks of birds, school of fish, and many similar assemblies of selfpropelled particles is the emergence of states of collective order in which the particles move in the same direction. When noise is added into the system, the onset of such collective order occurs through a dynamical phase transition controlled by the noise intensity. While originally thought to be continuous, the phase transition has been claimed to be discontinuous on the basis of recently reported numerical evidence. We address this issue by analyzing two representative network models closely related to systems of self-propelled particles. We present analytical as well as numerical results showing that the nature of the phase transition depends crucially on the way in which noise is introduced into the system. PACS numbers: 05.70. Fh, 87.17.Jj, The collective motion of a group of autonomous particles is a subject of intense research that has potential applications in biology, physics and engineering [1,2,3]. One of the most remarkable characteristics of systems such as a flock of birds, a school of fish or a swarm of locusts, is the emergence of ordered states in which the particles move in the same direction, in spite of the fact that the interactions between the particles are (presumably) of short range. Given that these systems are generally out of equilibrium, the emergence of ordered states cannot be accounted for by the standard theorems in statistical mechanics that explain the existence of ordered states in equilibrium systems typified by ferromagnets.A particularly simple model to describe the collective motion of a group of self-propelled particles was proposed by Vicsek et al. [4]. In this model each particle tends to move in the average direction of motion of its neighbors while being simultaneously subjected to noise. As the amplitude of the noise increases the system undergoes a phase transition from an ordered state in which the particles move collectively in the same direction, to a disordered state in which the particles move independently in random directions. This phase transition was originally thought to be of second order. However, due to a lack of a general formalism to analyze the collective dynamics of the Vicsek model, the nature of the phase transition (i.e. whether it is second or first order) has been brought into question [5].In this letter we show that the nature of the phase transition can depend strongly on the way in which the noise is introduced into these systems. We illustrate this by presenting analytical results on two different network systems that are closely related to the self-propelled particle models. We show that in these two network models the phase transition switches from second to first order when the way in which the noise is introduced changes from the one presented in [4] to the one described in [5].The first network model, which we will refer to as the vectorial network model, consists of a network of N 2D-vectors (represented as complex numbers), {σ 1 = e iθ...