Idiopathic generalised epilepsy (IGE) has a genetic basis. The mechanism of seizure expression is not fully known, but is assumed to involve large-scale brain networks. We hypothesised that abnormal brain network properties would be detected using EEG in patients with IGE, and would be manifest as a familial endophenotype in their unaffected first-degree relatives. We studied 117 participants: 35 patients with IGE, 42 unaffected first-degree relatives, and 40 normal controls, using scalp EEG. Graph theory was used to describe brain network topology in five frequency bands for each subject. Frequency bands were chosen based on a published Spectral Factor Analysis study which demonstrated these bands to be optimally robust and independent. Groups were compared, using Bonferroni correction to account for nonindependent measures and multiple groups. Degree distribution variance was greater in patients and relatives than controls in the 6-9 Hz band (p = 0.0005, p = 0.0009 respectively). Mean degree was greater in patients than healthy controls in the 6-9 Hz band (p = 0.0064). Clustering coefficient was higher in patients and relatives than controls in the 6-9 Hz band (p = 0.0025, p = 0.0013). Characteristic path length did not differ between groups. No differences were found between patients and unaffected relatives. These findings suggest brain network topology differs between patients with IGE and normal controls, and that some of these network measures show similar deviations in patients and in unaffected relatives who do not have epilepsy. This suggests brain network topology may be an inherited endophenotype of IGE, present in unaffected relatives who do not have epilepsy, as well as in affected patients. We propose that abnormal brain network topology may be an endophenotype of IGE, though not in itself sufficient to cause epilepsy.