在圖的探勘中，找到關係緊密的群體已經是一個基本課題，例如在分析社群網路、合作網路上，我們可以從中找出關係緊密的群體。可惜的是，在之前大部分的研究中，社群搜尋通常忽略了時間的資訊，可能因此少發現了很多有趣的群體。如果考慮了時間，那我們就可以獲得更多有用的資訊。
在本論文中，我們將研究如何於時序性網路中找到一個有密集互動的群體。在時序性網路中，每條邊會伴隨著一個時間標記，用來顯示此條邊會於何時出現，我們提出了一個模型叫(L, K)-lasting core，先用基本演算法找出最大的群體，再套用其他進階技巧來加快我們找出這個群體的時間。
我們在不同的資料集上進行實驗，結果驗證了我們方法的效率、有效性及可擴展性，確實是可以找到有著密集互動的群體。

Extracting dense subgroup is a fundamental task in graph mining. We can find dense subgroups from social networks and collaboration networks after analyzing them. Unfortunately, they usually ignored temporal information on community search in most previous research. Thus, some interesting groups may be undiscovered. If we consider the temporal information, we can receive more useful information.
In this paper, we study on finding a dense subgroup in temporal network. In a temporal network, each edge has a timestamp which means the time it appeared. We propose a model called (L, K)-lasting core. First, we use a baseline algorithm to find the maximum group and then apply other advanced techniques to speed up the searching time.
We conduct experiments on different datasets. The result demonstrates the scalability, efficiency and effectiveness of our methods. We can indeed find a group which members have intensive interactions.

1 Introduction 1
2 Related Work 4
2.1 Dense Subgraph 4
2.2 Multilayer Network 5
3 Problem Definition 7
4 Methods 9
4.1 Naive Algorithm 9
4.2 Temporal Core Finding-Basic (TCFB) 10
4.3 Min-Degree Pruning (MDP) 11
4.4 Reordering for Intersection Minimization (RIM) 12
4.5 Time complexity and optimality 15
5 Experiments 18
5.1 Optimal solution 19
5.2 Comparison of methods 21
5.3 Case study 25
6 Conclusions 27
References 28

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