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An irregularity index <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>I</mi><mi>R</mi><mo>(</mo><mi mathvariant="sans-serif">Γ</mi><mo>)</mo></mrow></semantics></math></inline-formula> of a graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Γ</mi></semantics></math></inline-formula> is a nonnegative numeric quantity (i.e., <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>I</mi><mi>R</mi><mo>(</mo><mi mathvariant="sans-serif">Γ</mi><mo>)</mo><mo>≥</mo><mn>0</mn></mrow></semantics></math></inline-formula>) such that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>I</mi><mi>R</mi><mo>(</mo><mi mathvariant="sans-serif">Γ</mi><mo>)</mo><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula> iff <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="sans-serif">Γ</mi></semantics></math></inline-formula> is a regular graph. In this paper, we show that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>I</mi><mi>R</mi><mi>C</mi></mrow></semantics></math></inline-formula> closely correlates with the normal boiling point <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mrow><mi>b</mi><mi>p</mi></mrow></msub></semantics></math></inline-formula> and the standard heat of formation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msubsup><mi>H</mi><mi>f</mi><mi>o</mi></msubsup></mrow></semantics></math></inline-formula> of lower benzenoid hydrocarbons. The correlation models that fit the data efficiently for both <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mrow><mi>b</mi><mi>p</mi></mrow></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msubsup><mi>H</mi><mi>f</mi><mi>o</mi></msubsup></mrow></semantics></math></inline-formula> are linear. We develop further mathematical properties of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>I</mi><mi>R</mi><mi>C</mi></mrow></semantics></math></inline-formula> by calculating its exact expressions for the recently introduced transformation graphs as well as certain derived graphs, such as the total graph, semi-total point graph, subdivision graph, semi-total line graph, double, strong double, and extended double cover graphs. Some open problems are proposed for further research on the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>I</mi><mi>R</mi><mi>C</mi></mrow></semantics></math></inline-formula> index of graphs.