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

• Published in: PloS one 2012-12, Vol.7 (12), p.e49949-e49949
• Main Authors: Takahashi, Daniel Yasumasa, Sato, João Ricardo, Ferreira, Carlos Eduardo, Fujita, André
• Format: Article
• Language: English
• Subjects: Analysis; Attention Deficit Disorder with Hyperactivity - diagnosis; Attention Deficit Disorder with Hyperactivity - metabolism; Attention deficit hyperactivity disorder; Biology; Brain; Care and treatment; Child; Children; Cluster Analysis; Clustering; Computational Biology - methods; Computer Graphics; Computer science; Divergence; Entropy; Graphs; Health aspects; Humans; Hypothesis testing; Magnetic Resonance Imaging; Mathematics; Medical treatment; Medicine; Metabolism; Modularity; Networks; Neural networks; Neurosciences; Norms; Parameter estimation; Population (statistical); Power; Prognosis; Protein interaction; Protein Interaction Maps; Protein-protein interactions; Proteins; ROC Curve; Social networks; Structure-function relationships; Topology
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0049949

The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world topology. Recent studies indicate that some pathologies present topological network alterations relative to norms seen in the general population. Therefore, methods to discriminate the processes that generate the different classes of networks (e.g., normal and disease) might be crucial for the diagnosis, prognosis, and treatment of the disease. It is known that several topological properties of a network (graph) can be described by the distribution of the spectrum of its adjacency matrix. Moreover, large networks generated by the same random process have the same spectrum distribution, allowing us to use it as a "fingerprint". Based on this relationship, we introduce and propose the entropy of a graph spectrum to measure the "uncertainty" of a random graph and the Kullback-Leibler and Jensen-Shannon divergences between graph spectra to compare networks. We also introduce general methods for model selection and network model parameter estimation, as well as a statistical procedure to test the nullity of divergence between two classes of complex networks. Finally, we demonstrate the usefulness of the proposed methods by applying them to (1) protein-protein interaction networks of different species and (2) on networks derived from children diagnosed with Attention Deficit Hyperactivity Disorder (ADHD) and typically developing children. We conclude that scale-free networks best describe all the protein-protein interactions. Also, we show that our proposed measures succeeded in the identification of topological changes in the network while other commonly used measures (number of edges, clustering coefficient, average path length) failed.