A topological index is a molecular index that converts molecular structures into specific real values. Chemical graph theory relies heavily on topological indices to build quantitative structure activity correlations in which attributes of molecules can be connected to their chemical structures. Chemical graph theory should be seen not only as equivalent to other fields of theoretical chemistry, but also as complementary and important for a deeper knowledge of the nature of chemical structure and helpful in modelling the networks. The main goal of this research work is to construct the line graph of octagonal network, then computing topological indices for the line graph of octagonal network which based on the degree of vertices and neighborhood degree of vertices. After that, we give graphically representation of the computed topological indices.