Neuroimaging research in surgically treated pediatric hydrocephalus patients remains challenging due to the artifact caused by programmable shunt. Our previous study has demonstrated significant alterations in the whole brain white matter structural connectivity based on diffusion tensor imaging (DTI) and graph theoretical analysis in children with hydrocephalus prior to surgery or in surgically treated children without programmable shunts. This study seeks to investigate the impact of brain injury on the topological features in the left hemisphere, contratelateral to the shunt placement, which will avoid the influence of shunt artifacts and makes further group comparisons feasible for children with programmable shunt valves. Three groups of children (34 in the control group, 12 in the 3-month post-surgery group, and 24 in the 12-month post-surgery group, age between 1 and 18 years) were included in the study. The structural connectivity data processing and analysis were performed based on DTI and graph theoretical analysis. Specific procedures were revised to include only left brain imaging data in normalization, parcellation, and fiber counting from DTI tractography. Our results showed that, when compared to controls, children with hydrocephalus in both the 3-month and 12-month post-surgery groups had significantly lower normalized clustering coefficient, lower small-worldness, and higher global efficiency (all p < 0.05, corrected). At a regional level, both patient groups showed significant alteration in one or more regional connectivity measures in a series of brain regions in the left hemisphere (8 and 10 regions in the 3-month post-surgery and the 12-month post-surgery group, respectively, all p < 0.05, corrected). No significant correlation was found between any of the global or regional measures and the contemporaneous neuropsychological outcomes [the General Adaptive Composite (GAC) from the Adaptive Behavior Assessment System, Second Edition (ABAS-II)]. However, one global network measure (global efficiency) and two regional network measures in the insula (local efficiency and between centrality) tested at 3-month post-surgery were found to correlate with GAC score tested at 12-month post-surgery with statistical significance (all p < 0.05, corrected). Our data showed that the structural connectivity analysis based on DTI and graph theory was sensitive in detecting both global and regional network abnormality when the analysis was conducted in the left hemisphere only. This approach provides a new avenue enabling the application of advanced neuroimaging analysis methods in quantifying brain damage in children with hydrocephalus surgically treated with programmable shunts.