在這篇論文裡，基於兩個簡單的節點行為模式，我們提出一個演算法來偵測大型網路中相互重疊的社群結構 (overlapping community structure)。在我們的演算法中，最主要的想法是讓一個節點形成的集合漸漸地增大(透過不斷地加入新的節點)，使得我們所偵測到的每一個節點集合S有以下的性質:對於S裡的每一個節點i，我們有 (1) 節點i所連接到的S之節點數目除以S之總節點數目大於一個門檻值，或者 (2) 節點i所連接到的S之節點數目除以節點i的分支度 (degree) 大於另一個門檻值。為了測試我們的演算法，我們用電腦產生出具有內建的相互重疊之社群結構的網路，並且將我們的演算法應用在這些網路，透過大量的測試，結果顯示我們的演算法有很好的表現。另外，我們也將我們的演算法應用在一個真實世界的網路「空手道社」上，在這個網路裡，我們的演算法所偵測到的社群結構非常接近這個網路已知的社群結構。

In this thesis, we propose an algorithm that detects overlapping communities in networks (graphs) based on two simple node behavior models. The key idea in our algorithm is to find communities in a local agglomerative manner such that every community S has the following property: For each node i in S we have (1) the fraction of nodes in S that are
connected to node i is greater than a given threshold, or (2) the fraction of edges of node i that are connected to S is greater than another given threshold. Through extensive computer simulations of random graphs with built-in overlapping community structure, including the LFR benchmark random graphs and Erd¨os-R´enyi type random graphs, we show that our simple algorithm has excellent performance. Furthermore, we apply our algorithm to the
real-world network “Karate club” and show that the overlapping communities detected by our algorithm are very close to the known communities in this graph.

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