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Studies of brain network organisation have swiftly adopted graph theory-based quantitative analysis of complicated networks. Small-world topology, densely connected hubs, and modularity characterise the brain’s structural and functional systems. Many measures quantify graph topology. It has not yet been determined which measurements are most appropriate for brain network analysis. This work introduces a new parameter applicable to brain network analysis. This parameter may help in the identification of symmetry and the study of symmetry breakdown in the brain. This is important because decreased symmetry in the brain is associated with a decreased chance of developing neurodevelopmental and psychiatric disorders. This work is to study brain networks using maximal independent set-based topological indices. These indices seem to depict significant properties of brain networks, such as clustering, small-worldness, etc. One new parameter introduced in this paper for brain network analysis depends on Zagreb topological indices and independence degree. This parameter is useful for analyzing clusters, rich clubs, small-worldness, and connectivity in modules.