Efficient Techniques for Graph Searching and Biological Network Mining

Graphs appear in several settings, like social networks, recommendation systems, computer communication networks, gene/protein biological networks, among others. A large amount of graph patterns, as well as graph generator models that mimic such patterns have been proposed over the last years. However, a deep and recurring question still remains: “What is a good pattern?” The answer is related to finding a pattern or a tool able to help distinguishing between actual real-world and fake graphs. Here we explore the ability of ShatterPlots, a simple and powerful algorithm to tease out patterns of real graphs, helping us to spot fake/masked graphs. The idea is to force a graph to reach a critical (“Shattering”) point, randomly deleting edges, and study its properties at that point.

From biochemical applications to social networks, graphs represent data. Comparing graphs or searching for motifs on such data often reveals interesting and useful patterns. Most of the problems on graphs are known to be NP-complete. Because of the computational complexity of subgraph matching, reducing the candidate graphs or restricting the space in which to search for motifs is critical to achieving efficiency. Therefore, to optimize and engineer isomorphism algorithms, design indexing and suitable search methods for large graphs are the main directions investigated in the graph searching area. This chapter focuses on the key concepts underlying the existing algorithms. First it reviews the most known used algorithms to compare two algorithms and then it describes the algorithms to search on large graphs making emphasis on their application on biological area.