九州工業大学博士学位論文（要旨） 学位記番号:情工博甲第296号 学位授与年月日:平成27年3月25

李 彦廷

A community in a graph is a group of nodes holding similar characteristics or sharing common properties within the graph. It is also referred to as a cluster or a module of graphs. A graph is considered to have the community structure if its nodes can be clustered into several subsets of nodes within a certain degree or density. The community structure is, therefore, one of the most relevant characteristics of graphs. The community structure has attracted tremendous interest in recent years for its various scientific applications. The community structure represents real world network systems, and models many kinds of real world relations, such as biological networks, web pages and social networks. Furthermore, the community structure can be used for analyzing the hierarchical organizations of real world network systems, and for understanding the structure of complicated network systems. Various efficient and effective techniques have been proposed and developed for identifying communities in graphs. Among various community extraction and graph analysis techniques, graph decomposition techniques play a vital role in identifying communities in graphs. The graph decomposition is to divide a graph into a set of dense subgraphs interpreted as communities so that the communities in the graph can be identified and extracted. Then, it is feasible and available to focus on smaller but more crucial areas of the graph when the input graph becomes exceedingly massive. As a definition of dense subgraph, the k-truss formed by triangles is one of the simplest cohesive subgraphs since triangle is the smallest non-trivial clique. By the definition, every edge of the dense subgraph to be decomposed is contained in at least (k .2)-triangle. The task of k-truss decomposition is to find all trusses in a graph. The cohesive subgraphs in a graph can be extracted hierarchically based on the k-truss decomposition method. A triangle (or 3-clique), consists of three fully connected nodes. It is the densest substructure in a graph. Therefore, the k-truss keeps a good trade-off between computational efficiency and clique approximation. However, the k-truss is not available for bipartite graphs because no triangle occurs in bipartite graphs. The k-truss decomposition method is not applicable to bipartite graphs. In this research, by adding additional edges to a bipartite graph, we extend the notion of k-truss to bipartite graphs, name it the quasi-k-truss, so that the communities as cohesive subgraphs can be extracted from a bipartite graph. Then, the original bipartite graph G is transformed to another graph G′. When a k-truss T is computed from G, the quasi-k-truss is the subgraph whose edges are included in both T and G′, that is, the graph obtained by removing all additional edges from T. Every edge in the quasi-k-truss is contained in at least (k-2)-triangle while a bipartite graph contains no triangles inside. In order to extract triangles virtually in a given bipartite graph, we introduce the auxiliary edges. Alternative to the originally existed edges, the auxiliary edges do not originally exist in bipartite graphs. An auxiliary edge is generated between any two nodes in the same node set if these two nodes share at least one common neighbor node in the other node set. The set of auxiliary edges is generated among all nodes with the same characteristics in a given bipartite graph. The set of auxiliary edges is generated for forming triangles in a given bipartite graph. According to the notion of quasi-k-truss of bipartite graphs, the quasi-k-truss decomposition algorithm is developed for decomposing a bipartite graph, and extracting communities represented by dense subgraphs from a bipartite graph. In the proposed algorithm, initially, a set of auxiliary edges is generated to form triangles in a given bipartite graph. Then, to extract communities from a bipartite graph, the number of triangles containing an edge of the bipartite graph is counted. Communities can be extracted hierarchically from a bipartite graph based on an iterated procedure. In order to improve the computational efficiency, some data structures have been applied to the implementation of the proposed algorithm. Finally, experiments for real world datasets have been conducted to verify the effectiveness and efficiency of the proposed method compared with baseline methods.九州工業大学博士学位論文 学位記番号:情工博甲第296号 学位授与年月日:平成27年3月25日1 Introduction|2 Community Extraction from Graphs|3 Quasi-k-truss Decomposition for Bipartite Graphs|4 Experiments and Evaluations|5 Conclusion and Future Work九州工業大学平成26年

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三角形数え上げに基づくグラフ分割手法によるコミュニティ抽出

Graph Decomposition Based on Triangle Countfor Community Extraction著者 李 彦廷発行年 2015-03-25その他のタイトル 三角形数え上げに基づくグラフ分割手法によるコミュニティ抽出学位授与番号 17104甲情工第296号URL http://hdl.handle.net/10228/5350 氏     名     李 彦廷（中国）  学 位 の 種 類       EA     博 士（情報工学）  A学 位 記 番 号       EA      情工博甲第２９６号  学位授与の日付      平成２７年３月２５日  学位授与の条件   学位規則第４条第１項該当  A学位論文題目       EA   Graph Decomposition Based on Triangle Count for Community Extraction (三角形数え上げに基づくグラフ分割手法によるコミュニティ抽出)  A論文審査委員       EA      主 査      教 授  坂本 比呂志                   〃   篠原 武                                    〃   平田 耕一                   〃     許 宗焄                   〃   久保山 哲二  学 位 論 文 内 容 の 要 旨 本研究は，ネットワーク構造からコミュニティと呼ばれる密な部分グラフを抽出するための手法を提案し，特に，二部グラフにおいて高い効果が得られることを示した．密な部分構造の計算は，時間的・領域的コストが大きく，その近似的な手法として，グラフに含まれる三角形を組み合わせるトーラス法と呼ばれる手法が注目されている．しかし，トーラス法は，適用するグラフのクラスによっては有効性を失ってしまうため，本研究ではトーラスの概念を拡張し，擬トーラスを定義した．本研究では，二部グラフに本来存在しない三角形を擬似的に作り出すことで擬トーラスを計算し，結果から疑似辺を取り除くことで密な部分構造を抽出することができる．本研究の最初の結果はこのようなアイディアに基づき，実データに対する実験によってその有効性が確認された．しかし本手法においても，本来抽出すべき部分グラフよりも密度が極端に低くなってしまう入力が存在する．そこで，さらに擬トーラスの改良手法を提案した．改良手法として，極端に多くの三角形に含まれる辺を予め取り除くルーチンを組み込むことで，これまで有効な解を得ることができなかった入力に対してもうまく働くことを示した．また，得られたコミュニティが十分な密度を保ち，それが自明な手法では発見できないことも比較実験によって示した．以上の結果により，本手法によってトーラス法を二部グラフに拡張することに成功した．よって本論文は，これまでにない新しい手法を提案している． 学 位 論 文 審 査 の 結 果 の 要 旨 本論文に関して，調査委員からコミュニティ抽出の意義や他手法に対する優位性に関する質問がなされたが，いずれも著者から満足な回答が得られた．また，公聴会においても，多数の出席があり，種々の質問がなされ，いずれも著者の説明によって質問者の理解が得られた．以上により，論文調査及び最終試験の結果に基づき，審査委員会において慎重に審査した結果，本論文が，博士（情報工学）の学位に十分値するものであると判断した． 

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三角形数え上げに基づくグラフ分割手法によるコミュニティ抽出

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Kyutacar : Kyushu Institute of Technology Academic Repository

Kyutacar : Kyushu Institute of Technology Academic Repository