(1) Background: Psychometric network analysis provides a novel statistical approach allowing researchers to model clusters of related symptoms as a dynamic system. This study applied network analysis to investigate the patterns of somatic, cognitive, and affective neurobehavioral symptoms in an international sample of Spanish-speaking individuals with a history of COVID-19 positivity and non-COVID controls; (2) methods: the sample (n = 1093) included 650 adults from 26 countries who reported having previously tested positive for COVID-19 (COVID+) through a viral and/or antigen test (average of 147 days since diagnosis). The control group (COVID-) was comprised of 443 adults from 20 countries who had completed the survey prior to the COVID-19 pandemic; (3) results: relative to the COVID- network, the COVID+ network was very well-connected, such that each neurobehavioral symptom was positively connected to the network. The organize-to-headache and dizzy-to-balance connections in the COVID+ network were stronger than in the COVID- network. The hearing, numbness, and tense symptoms were more central to the COVID+ network with the latter connected to the sleep, fatigue, and frustrated symptoms. The COVID- network was largely disjointed, with most of the somatosensory symptoms forming their own cluster with no connections to other symptom groups and fatigue not being connected to any other symptom. The cognitive and affective symptoms in the COVID- network were also largely connected to symptoms from within their own groups; (4) conclusions: These findings suggest that many of the long-term neurobehavioral symptoms of COVID-19 form a discernable network and that headaches, frustration, hearing problems, forgetfulness, and tension are the most central symptoms. Cognitive and behavioral rehabilitation strategies targeting these central symptom network features may hold promise to help fracture the lingering symptom network of COVID-19.