Objective: While scalp EEG is important for diagnosing epilepsy, a single routine EEG is limited in its diagnostic value. Only a small percentage of routine EEGs show interictal epileptiform discharges (IEDs) and overall misdiagnosis rates of epilepsy are 20-30%. We aim to demonstrate how analyzing network properties in EEG recordings can be used to improve the speed and accuracy of epilepsy diagnosis - even in the absence of IEDs. Methods: In this multicenter study, we analyzed routine scalp EEGs from 203 patients with suspected epilepsy and normal initial EEGs. The patients' diagnoses were later confirmed based on an epilepsy monitoring unit (EMU) admission. About 47% ultimately being diagnosed with epilepsy and 53% with non-epileptic conditions. A logistic regression model was trained using spectral and network-derived EEG features to differentiate between epilepsy and non-epilepsy. The model was trained using 10-fold cross-validation on 70% of the data, which was stratified to include equal numbers of epilepsy and non-epilepsy patients in both training and testing groups. The resulting tool was named EpiScalp. Results: EpiScalp achieved an area under the curve (AUC) of 0.87. The model had an accuracy of 0.78, a sensitivity of 0.86, and a specificity of 0.72 in classifying patients as having epilepsy or not. Interpretation: EpiScalp provides accurate diagnostic aid from a single initial EEG recording, even in more challenging epilepsy cases with normal initial EEGs. This may represent a paradigm shift in epilepsy diagnosis by deriving an objective measure of epilepsy likelihood from previously uninformative EEGs.