<p>The spectral graph theory plays a crucial role in representing graph theoretic information employing algebraic properties of specific matrices. Adjacency (<i>A</i>) and Laplacian (<i>L</i>) matrices are the most important tools in this discipline for uncovering thousands of secrets about graph theory and its applications. A massive amount of works on these matrices led to a contemporary trend of modifying them. The NBD Laplacian matrix <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L_{N}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>N</mi> </msub> </math></EquationSource> </InlineEquation> is proposed here as a useful extension of <i>L</i>. Fascinating mathematical features of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L_{N}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>N</mi> </msub> </math></EquationSource> </InlineEquation> are revealed by finding crucial bounds of its eigenvalues with characterizing extremal graphs. Role of this matrix spectrum in structure–property modelling of molecules is also demonstrated. The formulation of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(L_{N}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>N</mi> </msub> </math></EquationSource> </InlineEquation> matrix is not ad hoc; rather, its chemical significance exerts that it outperforms <i>L</i> in explaining physico-chemical properties of molecules and isomer discrimination, which is quite encouraging.</p>