Identification of crucial elements for network integrity: a perturbation approach through graph spectral method

The complex behaviour of a network emerges as a product of all the interactions between its components as a single entity. The aim of system level investigations has been to identify emergent properties of a network. Identifying crucial components which are responsible for maintaining integrity of networks is essential, to understand or control them. This study presents a method to rank the participation of nodes and edges in a network using perturbation analysis to identify crucial players that contribute to the integrity of the network. The spectra of a network capture maximal features with minimal loss of information. Unlike earlier methods which evaluate perturbation in a network, based on the change in centralities or paths, the present method uses a network comparison score (Network Similarity Score) which quantifies changes at edge level to global entity level using graph spectral properties. The method is evaluated on realistic complex networks of protein structures of Muscarinic acetylcholine receptors. The important amino acid residues (nodes) and their interactions (edges) derived from the study have been correlated with experimental findings. The potential of perturbation score as a predictive tool for any real-world network is also discussed.