## The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc. | |

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of
the Department of Computer Science and Engineering for public examination and debate in Auditorium
T1 at Helsinki University of Technology (Espoo, Finland) on the 28^{th} of April, 2006, at 12 o'clock noon.

Dissertation in PDF format (ISBN 951-22-8119-8) [4611 KB]

Dissertation is also available in print (ISBN 951-22-8118-X)

In this thesis, observations on structural properties of natural networks are taken as a starting point for developing efficient algorithms for natural instances of different graph problems. The key areas discussed are sampling, clustering, routing, and pattern mining for large, nonuniform graphs. The results include observations on structural effects together with algorithms that aim to reveal structural properties or exploit their presence in solving an interesting graph problem.

Traditionally networks were modeled with uniform random graphs, assuming that each vertex was equally important and each edge equally likely to be present. Within the last decade, the approach has drastically changed due to the numerous observations on structural complexity in natural networks, many of which proved the uniform model to be inadequate for some contexts.

This quickly lead to various models and measures that aim to characterize topological properties of different kinds of real-world networks also beyond the uniform networks. The goal of this thesis is to utilize such observations in algorithm design, in addition to empowering the process of network analysis. Knowing that a graph exhibits certain characteristics allows for more efficient storage, processing, analysis, and feature extraction.

Our emphasis is on local methods that avoid resorting to information of the graph structure that is not relevant to the answer sought. For example, when seeking for the cluster of a single vertex, we compute it without using any global knowledge of the graph, iteratively examining the vicinity of the seed vertex. Similarly we propose methods for sampling and spanning-tree construction according to certain criteria on the outcome without requiring knowledge of the graph as a whole.

Our motivation for concentrating on local methods is two-fold: one driving factor is the ever-increasing size of real-world problems, but an equally important fact is the nonuniformity present in many natural graph instances; properties that hold for the entire graph are often lost when only a small subgraph is examined.

**Keywords:**
community structure, graph algorithm, graph clustering, graph
data mining, graph similarity, local search, minimum spanning tree, network
model, nonuniform network, random graph, random sampling, routing,
scale-free network, shortest path algorithm, small-world network

This publication is copyrighted. You may download, display and print it for Your own personal use. Commercial use is prohibited.

© 2006 Helsinki University of Technology

Last update 2011-05-26