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The brain's structural and functional systems, protein-protein interaction,and gene networks are examples of biological systems that share some featuresof complex networks, such as highly connected nodes, modularity, andsmall-world topology. Recent studies indicate that some pathologies presenttopological network alterations relative to norms seen in the generalpopulation. Therefore, methods to discriminate the processes that generate thedifferent classes of networks (e.g., normal and disease) might be crucial forthe diagnosis, prognosis, and treatment of the disease. It is known thatseveral topological properties of a network (graph) can be described by thedistribution of the spectrum of its adjacency matrix. Moreover, large networksgenerated by the same random process have the same spectrum distribution,allowing us to use it as a "fingerprint". Based on this relationship, weintroduce and propose the entropy of a graph spectrum to measure the"uncertainty" of a random graph and the Kullback-Leibler and Jensen-Shannondivergences between graph spectra to compare networks. We also introducegeneral methods for model selection and network model parameter estimation, aswell as a statistical procedure to test the nullity of divergence between twoclasses of complex networks. Finally, we demonstrate the usefulness of theproposed methods by applying them on (1) protein-protein interaction networksof different species and (2) on networks derived from children diagnosed withAttention Deficit Hyperactivity Disorder (ADHD) and typically developingchildren. We conclude that scale-free networks best describe all theprotein-protein interactions. Also, we show that our proposed measuressucceeded in the identification of topological changes in the network whileother commonly used measures (number of edges, clustering coefficient, averagepath length) failed.

Discriminating different classes of biological networks by analyzing the graphs spectra distribution