Sequence alignment is based on computeroriented and computer-intensive comparisons of sequences, and then a distance function or a score function is obtained. Using the distance function, one can compare biological sequences. However, multiple sequence alignment of several hundred sequences always produces a bottleneck, firstly due to long computational time, and secondly due to possible bias of multiple sequence alignments for multiple occurrences of highly similar sequences (Pham and Zuegg, 2004) . Therefore, the emergence of a study on alignment-free sequence analysis is obvious. Until now, alignment-free sequence analysis is still in its early development. For most alignment-free methods, a biological sequence should be transformed into an object for which a linear algebra and statistical theory already has useful analytical tools. Since 1983, DNA sequence has been represented in different dimension spaces (Hamori and Ruskin, 1983; Hamori, 1985; Nandy, 1994; 1996; Nandy and Basak, 2000; Randić et al., 2001; Randić, 2003; Randić and Balaban, 2003; Zhang et al., 2003; Liao and Wang, 2004; Liao et al., 2005; Nandy et al., 2006; Bai et al., 2007; Feng and Wang, 2008) . Each nucleotide of a given DNA sequence is a point in different dimension spaces, and these graphical representations can allow us to qualitatively analyze DNA sequences, and provide a way of viewing, sorting and comparing various genomic sequences. Based on the graphical representation, it is possible to numerically characterize DNA sequence and further quantitatively measure similarity of different DNA sequences. Although protein sequence and DNA sequence belong to symbolic sequences, compared with DNA sequence, there are fewer methods for the graphical representation of protein sequence. This is mainly because extension of DNA graphical representation to protein sequences would enormously increase the number of possible alternative assignments for the 20 amino acids. The amino acid sequence is the key to understanding protein structure and function in the cell, so analysis of amino acid sequence is an important part of post-genomic studies. Recently, several schemes have been proposed in protein graphical representation (Randić and Krilov, 1997; Vinga and Almeida, 2003; Bai and Wang, 2005; Li J. et al., 2006; Li C. et al., 2008; Munteanu et al., 2008; Yau et al., 2008; Yao et al., 2008; Wen and Zhang, 2009) . In order to plot amino acid sequence, 20 amino acids in protein sequences are divided into different types, including protein sequence regarded as a word with three, four, or five different letters. Since ordering amino acids based on their physicochemical properties may offer better insights into comparative study of protein than representation of protein based on the random ordering of amino acid, Randić (2007) and Yao et al. (2008; outlined different 2D graphical representations of protein sequence based on different physicochemical properties. The graphical representation of protein sequence cannot only describe amino acid sequence, but also measure similarity/ dissimilarity of different protein sequences. However, the methods only consider the string's information of protein, and do not consider adjacent string's information of amino acid sequence. Here, we choose conditional probability to measure adjacent string's information.