C(i,j) matrix: A better numerical characterization for graphical representations of biological sequences

We find that the traditional numerical characterizations of biological sequences, such as E matrix, D/D matrix, L/L matrix and their “high order” matrices, have their limitations to characterize the biological sequences exactly, but they are widely used to analyze the biological sequences. Here, we propose a better numerical characterization for graphical representations of biological sequences, C(i,j) matrix. It is associated with the curvature of every point and has many advantages: (1) It can characterize the graphical representations for DNA sequences exactly, because it can overcome the limitation of the traditional matrices. (2) If we choose an appropriate fixed point, we can make the elements of the C(i,j) matrix less than or equal to 1.