Detection of hypsarrhythmia electroencephalography (EEG) in infants with West syndrome (WS) is currently performed by manual inspection of long-term video/EEG recording, producing low inter-rater reliability. Existing studies aiming at exploring digital biomarkers for hypsarrhythmia EEG focus mainly on the temporal and spectral features. The aim of the present study is to explore the spatial distribution and connection of hypsarrhythmia EEG by analysing the brain functional connectivity (BFC) of WS patients and thus to identify possible biomarkers for hypsarrhythmia EEG. To this end, hypsarrhythmia and non-hypsarrhythmia EEG segments were extracted from 107 WS patients, and normal EEG segments were extracted from 155 healthy controls (HCs). Five connectivity metrics, including Pearson correlation coefficient, phase locking value, phase lag index, magnitude-squared coherence (MSC), and time-frequency cross mutual information (TFCMI), were utilized to build the BFC in different EEG sub-bands. Besides, graph theory was employed to estimate the topological parameters of each network, including clustering coefficient, characteristic path length, global efficiency, and local efficiency. Our results show enhanced brain connectivity in WS patients during hypsarrhythmia periods as compared with non-hypsarrhythmia and HCs. The statistical analysis determines significant difference ( ${p}\lt {0}.{05}$ ) in a number of network topological parameters, particularly derived from MSC- and TFCMI-based networks, between hypsarrhythmia EEG and non-hypsarrhythmia EEG or HCs. These findings suggest the BFC topology parameters to be promising biomarkers for hypsarrhythmia detection, possibly leading to the development of automatic tools for efficient and reliable WS diagnosis.