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Severe thunderstorms are a manifestation of deep convection. Conditional instability is known to be the mechanism by which thunderstorms are formed. The energy that drives conditional instability is convective available potential energy (CAPE), which is computed with radio sonde data at each pressure level. The purpose of the present paper is to identify the pattern or shape of CAPE required for the genesis of severe thunderstorms over Kolkata (22°32′N, 88°20′E) confined within the northeastern part (20°N to 24°N latitude, 85°E to 93°E longitude) of India. The method of chaotic graph theory is adopted for this purpose. Chaotic graphs of pressure levels and CAPE are formed for thunderstorm and non-thunderstorm days. Ranks of the adjacency matrices constituted with the union of chaotic graphs of pressure levels and CAPE are computed for thunderstorm and non-thunderstorm days. The results reveal that the rank of the adjacency matrix is maximum for non-thunderstorm days and a column with all zeros occurs very quickly on severe thunderstorms days. This indicates that CAPE loses connectivity with pressure levels very early on severe thunderstorm days, showing that for the genesis of severe thunderstorms over Kolkata short, and therefore broad, CAPE is preferred. [ABSTRACT FROM AUTHOR]