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A Thesis Submitted in Partial Fulfillment of the Requirement for the Degree of Master of Science in Computer Engineering

Karimi, Saeed | 2017

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 49928 (19)
  4. University: Sharif University of Technology
  5. Department: Computer Engineering
  6. Advisor(s): Beigi, Hamid
  7. Abstract:
  8. The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. One of the most practical methods of graph clustering is clustering based on quality functions. This means that by providing an optimization algorithm based on the quality functions, a good clustering of the graph is obtained. In this study, we describe quality functions for clustering graphs and offer a set of axioms for clustering graph. If a quality function meet more of these axioms, this quality function is better. We also try to improve these quality functions in order to require them to meet more of these axioms. According the betweenness clustering function, we desing a quality function and examine the axioms on this quality function. At the end we introduce a quality function with parameter based on cut clustering family and prove that this quality function meets all the axioms we presented in this thesis
  9. Keywords:
  10. Graph Clustering ; Clustering ; Quality Function ; Axioms ; Axiomatic Fromework

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