Triangle enumeration is an important element in graph analysis, and because of this it is a topic that has been studied extensively. Although the formulation is simple, for large networks the computation becomes challenging as we have to deal with memory limitation and efficiency. Many algorithms have been proposed to overcome these problems. Some use distributed computing, where the computation is distributed among many machines in a cluster. However, this approach has a high cost in terms of hardware resources and energy. In this thesis we studied triangle counting/listing algorithms for both directed and undirected graphs, and searched for methods to do the computation on a single machine. Through detailed analysis, we found some ways to improve the efficiency of the computation. Programs that implement the algorithms were built and tested on large networks with up to almost a billion nodes. The results were then analysed and discussed. / Graduate

abstract: Measuring node centrality is a critical common denominator behind many important graph mining tasks. While the existing literature offers a wealth of different node centrality measures, it remains a daunting task on how to intervene the node centrality in a desired way. In this thesis, we study the problem of minimizing the centrality of one or more target nodes by edge operation. The heart of the proposed method is an accurate and efficient algorithm to estimate the impact of edge deletion on the spectrum of the underlying network, based on the observation that the edge deletion is essentially a local, sparse perturbation to the original network. Extensive experiments are conducted on a diverse set of real networks to demonstrate the effectiveness, efficiency and scalability of our approach. In particular, it is average of 260.95%, in terms of minimizing eigen-centrality, better than the standard matrix-perturbation based algorithm, with lower time complexity. / Dissertation/Thesis / Masters Thesis Computer Science 2016