Background: Personality disorders show strong comorbidities with alcohol-use disorder (AUD), and several personality traits have been found to be more frequent in people with AUD. This study analyzes which personality facets of those proposed in the Alternative Model of Personality Disorder (AMPD) of DSM-5 are associated with the diagnostic criteria of AUD. Methods: The sample was composed of 742 participants randomly selected from the Spanish population, and 243 patients attending mental health services. All participants were of legal age and signed an informed consent form. The instruments were administered to the community sample in an online format, and a psychologist conducted individual face-to-face interviews with the patients. AMPD facets were assessed through the Personality Inventory of DSM-5 Short-Form, and the AUD criteria through the Substance Dependence Severity Scale. A network analysis was applied to identify the personality facets mostly associated with the AUD criteria. Results: The network analysis showed the existence of three communities, grouping the AUD criteria, externalizing spectrum facets, and internalizing spectrum facets, respectively. Risk taking, callousness, and irresponsibility facets showed the strongest association with the AUD criteria, bridging externalizing personality traits with AUD criteria. Conclusions: The facets of risk taking, callousness, and irresponsibility should be accurately assessed in patients with AUD to differentiate between a possible primary personality disorder and a syndrome induced by alcohol addiction.