The nonlinearity and fear hypothesis predicts that the structure of alarm vocalizations will be influenced by the signaller's internal state. Specifically, stressed or otherwise more aroused individuals will produce alarm calls that are relatively more nonlinear (i.e. they sound noisier). The position of an individual in a social network can influence an individual's sense of security. More centrally located individuals may feel more secure and thus we might expect that they would produce noisier calls. Building on previous research about the influence of social relationships on an individual's sense of security, we asked whether social network position explained variation in the noisiness (quantified as Wiener entropy) and goodness of pitch of alarm calls produced by trapped yellow-bellied marmots, Marmota flaviventer. More socially isolated individuals, characterized by lower instrength, produced alarm calls with higher entropy and higher goodness of pitch. These isolated individuals may be more aroused because they have fewer social partners to depend on when presented with a predatory threat; therefore, they produce both noisy and potentially louder calls. Additionally, individuals with higher outcloseness produced calls with higher goodness of pitch, which may be indicative of their ability to better inform neighbours of impending threats. Overall, this study further illustrates how an individual's social network position influences the structure of its alarm calls, which could reflect how individuals perceive their current safety levels.