Language change is neutral if the probability of a language learner adopting any given linguistic variant only depends on the frequency of that variant in the learner’s environment. Ruling out non-neutral motivations of change, be they sociolinguistic, computational, articulatory or functional, a theory of neutral change insists that at least some instances of language change are essentially due to random drift, demographic noise and the social dynamics of finite populations; consequently, it has remained little investigated in the historical and sociolinguistics literature, which has generally been on the lookout for more substantial causes of change. Indeed, recent computational studies have argued that a neutral mechanism cannot give rise to ‘well-behaved’ time series of change which would align with historical data, for instance to generate S-curves. In this paper, I point out a methodological shortcoming of those studies and introduce a mathematical model of neutral change which represents the language community as a dynamic, evolving network of speakers. With computer simulations and a quantitative operationalization of what it means for change to be well-behaved, I show that this model exhibits well-behaved neutral change provided that the language community is suitably clusterized. Thus, neutral change is not only possible but is in fact a characteristic emergent property of a class of social networks. From a theoretical point of view, this finding implies that neutral theories of change deserve more (serious) consideration than they have traditionally received in diachronic and variationist linguistics. Methodologically, it urges that if change is to be successfully modelled, some of the traditional idealizing assumptions employed in much mathematical modelling must be done away with.