Graph Theory and Networks in Biology

In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of bio-molecular networks, as well as the application of centrality measures to interaction networks and research on the hierarchical structure of such networks and network motifs. Work on the link between structural network properties and dynamics is also described, with emphasis on synchronization and disease propagation.Comment: 52 pages, 5 figures, Survey Pape

Analysis of group evolution prediction in complex networks

In the world, in which acceptance and the identification with social communities are highly desired, the ability to predict evolution of groups over time appears to be a vital but very complex research problem. Therefore, we propose a new, adaptable, generic and mutli-stage method for Group Evolution Prediction (GEP) in complex networks, that facilitates reasoning about the future states of the recently discovered groups. The precise GEP modularity enabled us to carry out extensive and versatile empirical studies on many real-world complex / social networks to analyze the impact of numerous setups and parameters like time window type and size, group detection method, evolution chain length, prediction models, etc. Additionally, many new predictive features reflecting the group state at a given time have been identified and tested. Some other research problems like enriching learning evolution chains with external data have been analyzed as well

Outlier Edge Detection Using Random Graph Generation Models and Applications

Outliers are samples that are generated by different mechanisms from other normal data samples. Graphs, in particular social network graphs, may contain nodes and edges that are made by scammers, malicious programs or mistakenly by normal users. Detecting outlier nodes and edges is important for data mining and graph analytics. However, previous research in the field has merely focused on detecting outlier nodes. In this article, we study the properties of edges and propose outlier edge detection algorithms using two random graph generation models. We found that the edge-ego-network, which can be defined as the induced graph that contains two end nodes of an edge, their neighboring nodes and the edges that link these nodes, contains critical information to detect outlier edges. We evaluated the proposed algorithms by injecting outlier edges into some real-world graph data. Experiment results show that the proposed algorithms can effectively detect outlier edges. In particular, the algorithm based on the Preferential Attachment Random Graph Generation model consistently gives good performance regardless of the test graph data. Further more, the proposed algorithms are not limited in the area of outlier edge detection. We demonstrate three different applications that benefit from the proposed algorithms: 1) a preprocessing tool that improves the performance of graph clustering algorithms; 2) an outlier node detection algorithm; and 3) a novel noisy data clustering algorithm. These applications show the great potential of the proposed outlier edge detection techniques.Comment: 14 pages, 5 figures, journal pape

GraphCrunch 2: Software tool for network modeling, alignment and clustering

<p>Abstract</p> <p>Background</p> <p>Recent advancements in experimental biotechnology have produced large amounts of protein-protein interaction (PPI) data. The topology of PPI networks is believed to have a strong link to their function. Hence, the abundance of PPI data for many organisms stimulates the development of computational techniques for the modeling, comparison, alignment, and clustering of networks. In addition, finding representative models for PPI networks will improve our understanding of the cell just as a model of gravity has helped us understand planetary motion. To decide if a model is representative, we need quantitative comparisons of model networks to real ones. However, exact network comparison is computationally intractable and therefore several heuristics have been used instead. Some of these heuristics are easily computable "network properties," such as the degree distribution, or the clustering coefficient. An important special case of network comparison is the network alignment problem. Analogous to sequence alignment, this problem asks to find the "best" mapping between regions in two networks. It is expected that network alignment might have as strong an impact on our understanding of biology as sequence alignment has had. Topology-based clustering of nodes in PPI networks is another example of an important network analysis problem that can uncover relationships between interaction patterns and phenotype.</p> <p>Results</p> <p>We introduce the GraphCrunch 2 software tool, which addresses these problems. It is a significant extension of GraphCrunch which implements the most popular random network models and compares them with the data networks with respect to many network properties. Also, GraphCrunch 2 implements the GRAph ALigner algorithm ("GRAAL") for purely topological network alignment. GRAAL can align any pair of networks and exposes large, dense, contiguous regions of topological and functional similarities far larger than any other existing tool. Finally, GraphCruch 2 implements an algorithm for clustering nodes within a network based solely on their topological similarities. Using GraphCrunch 2, we demonstrate that eukaryotic and viral PPI networks may belong to different graph model families and show that topology-based clustering can reveal important functional similarities between proteins within yeast and human PPI networks.</p> <p>Conclusions</p> <p>GraphCrunch 2 is a software tool that implements the latest research on biological network analysis. It parallelizes computationally intensive tasks to fully utilize the potential of modern multi-core CPUs. It is open-source and freely available for research use. It runs under the Windows and Linux platforms.</p