Phenotypic integration describes the complex interrelationships between organismal traits, traditionally focusing on morphology. Recently, research has sought to represent behavioural phenotypes as composed of quasi-independent latent traits. Concurrently, psychologists have opposed latent variable interpretations of human behaviour, proposing instead a network perspective envisaging interrelationships between behaviours as emerging from causal dependencies. Network analysis could also be applied to understand integrated behavioural phenotypes in animals. Here, we assimilate this cross-disciplinary progression of ideas by demonstrating the use of network analysis on survey data collected on behavioural and motivational characteristics of police patrol and detection dogs (Canis lupus familiaris). Networks of conditional independence relationships illustrated a number of functional connections between descriptors, which varied between dog types. The most central descriptors denoted desirable characteristics in both patrol and detection dog networks, with ‘Playful’ being widely correlated and possessing mediating relationships between descriptors. Bootstrap analyses revealed the stability of network results. We discuss the results in relation to previous research on dog personality, and benefits of using network analysis to study behavioural phenotypes. We conclude that a network perspective offers widespread opportunities for advancing the understanding of phenotypic integration in animal behaviour.