Mining and analysis of real-world graphs

Networked systems are everywhere - such as the Internet, social networks, biological networks, transportation networks, power grid networks, etc. They can be very large yet enormously complex. They can contain a lot of information, either open and transparent or under the cover and coded. Such real-world systems can be modeled using graphs and be mined and analyzed through the lens of network analysis. Network analysis can be applied in recognition of frequent patterns among the connected components in a large graph, such as social networks, where visual analysis is almost impossible. Frequent patterns illuminate statistically important subgraphs that are usually small enough to analyze visually. Graph mining has different practical applications in fraud detection, outliers detection, chemical molecules, etc., based on the necessity of extracting and understanding the information yielded. Network analysis can also be used to quantitatively evaluate and improve the resilience of infrastructure networks such as the Internet or power grids. Infrastructure networks directly affect the quality of people\u27s lives. However, a disastrous incident in these networks may lead to a cascading breakdown of the whole network and serious economic consequences. In essence, network analysis can help us gain actionable insights and make better data-driven decisions based on the networks. On that note, the objective of this dissertation is to improve upon existing tools for more accurate mining and analysis of real-world networks --Abstract, page iv

FSMS: A Frequent Subgraph Mining Algorithm using Mapping Sets

With the increasing prevalence of data that model relationships between various entities, the use of a graph-based representation for real-world problems offers a logical strategy for organizing information and making knowledge-based decisions. In particular, often it is useful to identify the most frequent patterns or relationships amongst the data in a graph, which requires finding frequent subgraphs. Algorithms for addressing that problem have been proposed for over 15 years. In the worst case, all subgraphs in the graph must be examined, which is exponential in complexity, and subgraph isomorphisms must be computed, which is an NP-complete problem. Frequent subgraph algorithms may attempt to improve the actual runtime performance by reducing the size of the search space, avoiding duplicate comparisons, and/or minimizing the amount of memory required for compiling intermediate results. Herein we present a frequent subgraph mining algorithm that leverages mapping sets in order to eliminate the isomorphism computation during the search for non-edge-disjoint frequent subgraphs. Experimental results show that absence of isomorphism computation leads to much faster frequent subgraph detection when there is a need to identify all occurrences of those subgraphs

Interactive Visualization of Robustness Enhancement in Scale-free Networks with Limited Edge Addition (RENEA)

Error tolerance and attack vulnerability of scale-free networks are usually used to evaluate the robustness of these networks. While new forms of attacks are developed everyday to compromise infrastructures, service providers are expected to develop strategies to mitigate the risk of extreme failures. Recently, much work has been devoted to design networks with optimal robustness, whereas little attention has been paid to improve the robustness of existing ones. Herein we present RENEA, a method to improve the robustness of a scale-free network by adding a limited number of edges. While adding an edge to a network is an expensive task, our system, during each iteration, allows the user to select the best option based on the cost, amongst all proposed ones. The edge-addition interactions are performed through a visual user interface while the algorithm is running. RENEA is designed based on the evolution of the network\u27s largest component during a sequence of targeted attacks. Through experiments on synthetic and real-life data sets, we conclude that applying RENEA on a scale-free network while interacting with the user can significantly improve its attack survivability at the lowest cost