The aim of the present study is to forecast thunderstorms over Kolkata (22°32'N, 88°20'E), India, during the pre-monsoon season (April-May) with graph spectral distance and entropy analysis. Graph vertices represent points connected by lines or edges, and lifting condensation level, convective condensation level, level of free convection, freezing level, level of neutral buoyancy and the surface level are taken as the input of the graph vertices. The variation in the most probable distance between the vertices is investigated. The result reveals a particular orientation of the vertex distances for thunderstorm days which is significantly different from the non-thunderstorm days. The reference graphs for thunderstorm and non-thunderstorm days are formed using the most probable vertex distances. The spectral distance between the reference graph and the graphs corresponding to thunderstorms are computed with the data collected during the period 1997-2009. The entropies, or the measure of disorderliness or uncertainty, are estimated for the graph distance matrices. The result shows that the thunderstorm days possess lower distance entropy than the non-thunderstorm days. This indicates that the reference graph that has been constructed for thunderstorms is more consistent. The result further depicts that the forecast accuracy through the present method is 98% with 1 h lead time, whereas the accuracy is 93% with 6 h lead time. The forecast is validated with the India Meteorological Department observations for the years 2007, 2008 and 2009. © 2011 Royal Meteorological Society.