Background and aims: Graph theoretic analysis of structural covariance networks (SCN) provides an assessment of brain organization that has not yet been applied to alcohol dependence (AD). We estimated whether SCN differences are present in adults with AD and heavy-drinking adolescents at age 19 and age 14, prior to substantial exposure to alcohol. Design: Cross-sectional sample of adults and a cohort of adolescents. Correlation matrices for cortical thicknesses across 68 regions were summarized with graph theoretic metrics. Setting and participants: A total of 745 adults with AD and 979 non-dependent controls from 24 sites curated by the Enhancing NeuroImaging Genetics through Meta Analysis (ENIGMA)–Addiction consortium, and 297 hazardous drinking adolescents and 594 controls at ages 19 and 14 from the IMAGEN study, all from Europe. Measurements: Metrics of network segregation (modularity, clustering coefficient and local efficiency) and integration (average shortest path length and global efficiency). Findings: The younger AD adults had lower network segregation and higher integration relative to non-dependent controls. Compared with controls, the hazardous drinkers at age 19 showed lower modularity [area-under-the-curve (AUC) difference = −0.0142, 95% confidence interval (CI) = −0.1333, 0.0092; P-value = 0.017], clustering coefficient (AUC difference = −0.0164, 95% CI = −0.1456, 0.0043; P-value = 0.008) and local efficiency (AUC difference = −0.0141, 95% CI = −0.0097, 0.0034; P-value = 0.010), as well as lower average shortest path length (AUC difference = −0.0405, 95% CI = −0.0392, 0.0096; P-value = 0.021) and higher global efficiency (AUC difference = 0.0044, 95% CI = −0.0011, 0.0043; P-value = 0.023). The same pattern was present at age 14 with lower clustering coefficient (AUC difference = −0.0131, 95% CI = −0.1304, 0.0033; P-value = 0.024), lower average shortest path length (AUC difference = −0.0362, 95% CI = −0.0334, 0.0118; P-value = 0.019) and higher global efficiency (AUC difference = 0.0035, 95% CI = −0.0011, 0.0038; P-value = 0.048). Conclusions: Cross-sectional analyses indicate that a specific structural covariance network profile is an early marker of alcohol dependence in adults. Similar effects in a cohort of heavy-drinking adolescents, observed at age 19 and prior to substantial alcohol exposure at age 14, suggest that this pattern may be a pre-existing risk factor for problematic drinking.