Irregularity measures of graphs serve as crucial tools for optimizing networks, understanding biological interactions, analyzing social dynamics, enhancing cybersecurity, and assessing market stability, offering valuable insights across diverse fields. In this paper, we introduce a family of irregularity measures for graphs with non-increasing degree sequences, termed degree scaling irregularities, defined as \(\mathcal {I}(G,r)=\sum _{i=1}^n d_i r_i\) , where \(d=(d_1,d_2,\) \(\ldots ,d_n)\) is a non-increasing degree sequence of a graph G and \(r = (r_1, r_2, \ldots , r_n)\) is a non-increasing n-tuple of real numbers such that \(r_1+r_2+ \cdots + r_n=0\) . This family provides a versatile framework for analyzing graph irregularity. Various choices for r are explored, including using eigenvalues of matrices related to G or orientations of G. It has been proven that if G maximizes \(\mathcal {I}\) -irregularity among all connected graphs of order n for a given r, then G is a split graph, a graph comprised of a clique and an independent set. Additionally, we investigate the properties of graphs that maximize \(\mathcal {I}\) -irregularity and explore computational aspects when r is based on matrix eigenvalues.
