Node similarity is a fundamental problem in graph analytics. However, node similarity between nodes in different graphs (inter-graph nodes) has not received a lot of attention yet. The inter-graph node similarity is important in learning a new graph based on the knowledge of an existing graph (transfer learning on graphs) and has applications in biological, communication, and social networks. In this paper, we propose a novel distance function for measuring inter-graph node similarity with edit distance, called NED. In NED, two nodes are compared according to their local neighborhood structures which are represented as unordered k-adjacent trees, without relying on labels or other assumptions. Since the computation problem of tree edit distance on unordered trees is NP-Complete, we propose a modified tree edit distance, called TED*, for comparing neighborhood trees. TED* is a metric distance, as the original tree edit distance, but more importantly, TED* is polynomially computable. As a metric distance, NED admits efficient indexing, provides interpretable results, and shows to perform better than existing approaches on a number of data analysis tasks, including graph de-anonymization. Finally, the efficiency and effectiveness of NED are empirically demonstrated using real-world graphs.
Another method that has been used for comparing biological networks, such as protein-protein interaction networks (PPI) and metabolic networks, is to extract a feature vector using graphlets @cite_21 @cite_3 . Graphlets are small connected non-isomorphic induced subgraphs of a large network @cite_10 and generalize the notion of the degree of a node. However, they are also limited to the small neighborhood around each node and as the size of the neighborhood increases the accuracy of this method decreases.
@cite_21 @cite_10 @cite_3
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Motivation: Discovering and understanding patterns in networks of protein–protein interactions (PPIs) is a central problem in systems biology. Alignments between these networks aid functional understanding as they uncover important information, such as evolutionary conserved pathways, protein complexes and functional orthologs. A few methods have been proposed for global PPI network alignments, but because of NP-completeness of underlying sub-graph isomorphism problem, producing topologically and biologically accurate alignments remains a challenge. Results: We introduce a novel global network alignment tool, Lagrangian GRAphlet-based ALigner (L-GRAAL), which directly optimizes both the protein and the interaction functional conservations, using a novel alignment search heuristic based on integer programming and Lagrangian relaxation. We compare L-GRAAL with the state-of-the-art network aligners on the largest available PPI networks from BioGRID and observe that L-GRAAL uncovers the largest common sub-graphs between the networks, as measured by edge-correctness and symmetric sub-structures scores, which allow transferring more functional information across networks. We assess the biological quality of the protein mappings using the semantic similarity of their Gene Ontology annotations and observe that L-GRAAL best uncovers functionally conserved proteins. Furthermore, we introduce for the first time a measure of the semantic similarity of the mapped interactions and show that L-GRAAL also uncovers best functionally conserved interactions. In addition, we illustrate on the PPI networks of baker's yeast and human the ability of L-GRAAL to predict new PPIs. Finally, L-GRAAL's results are the first to show that topological information is more important than sequence information for uncovering functionally conserved interactions. Availability and implementation: L-GRAAL is coded in C++. Software is available at: http: bio-nets.doc.ic.ac.uk L-GRAAL . Contact: ku.ca.lairepmi@ningod-dolam.n Supplementary information: Supplementary data are available at Bioinformatics online. Motivation: Networks have been used to model many real-world phenomena to better understand the phenomena and to guide experiments in order to predict their behavior. Since incorrect models lead to incorrect predictions, it is vital to have as accurate a model as possible. As a result, new techniques and models for analyzing and modeling real-world networks have recently been introduced. Results: One example of large and complex networks involves protein--protein interaction (PPI) networks. We analyze PPI networks of yeast Saccharomyces cerevisiae and fruitfly Drosophila melanogaster using a newly introduced measure of local network structure as well as the standardly used measures of global network structure. We examine the fit of four different network models, including Erdos-Renyi, scale-free and geometric random network models, to these PPI networks with respect to the measures of local and global network structure. We demonstrate that the currently accepted scale-free model of PPI networks fails to fit the data in several respects and show that a random geometric model provides a much more accurate model of the PPI data. We hypothesize that only the noise in these networks is scale-free. Conclusions: We systematically evaluate how well-different network models fit the PPI networks. We show that the structure of PPI networks is better modeled by a geometric random graph than by a scale-free model. Supplementary information: Supplementary information is available at http: www.cs.utoronto.ca juris data data ppiGRG04