Abstract Motivation Genes function in networks are typically correlated due to their functional connectivity. Variable selection methods have been developed to select important genes associated with a trait while incorporating network graphical information. However, no method has been proposed to quantify the uncertainty of individual genes under such settings. Results In this paper, we construct confidence intervals and provide p-values for parameters of a high-dimensional linear model incorporating graphical structures where the number of variables p diverges with the number of observations. For combining the graphical information, we propose a graph-constrained desparsified LASSO (GCDL) estimator, which reduces dramatically the influence of high correlation of predictors and enjoys the advantage of faster computation and higher accuracy compared with the desparsified LASSO. Theoretical results show that the GCDL estimator achieves asymptotic normality. The asymptotic property of the uniform convergence is established, with which an explicit expression of the uniform confidence interval can be derived. Extensive numerical results indicate that the GCDL estimator and its (uniform) confidence interval performs well even when predictors are highly correlated. Availability and implementation An R package implementing the proposed method is available at https://github.com/XiaoZhangryy/gcdl. Supplementary information Supplementary data are available at Bioinformatics online.