在最近的研究中，社群偵測是個熱門的議題，然而，如果我們只想注重在某些特定的點，或是某個特定的區域時，我們就需要區域社群偵測了。除此之外，如果網路結構是有方向性的，就像是引用網路，那也會產生很大的區別。因此我們提供了一個新方法，那就是使用相對重要性來在有方向性網路上做偵測。我們修改了之前的結構來適用於新的有方向性網路上。我們會使用兩種隨機漫步，並顯示如果我們使用通用型的兩部內隨機漫步會比使用只能走一部的簡單隨機漫步來的更好。經過實驗後，我們的方法能找到更大的社群數目且相信我們的加入順序會比只使用引用數目來當依據來的更有意義，這是因為我們把三角形列入考慮，這代表我們優先加入的那些點，並不只有引用原先的論文，更引用了許多那些有引用原本論文的論文。因此我們相信這個結構會更加的緊密且連結性更大。

Currently, the community detection in networks has gathered a lot of attention. How-
ever, if we are only interested in certain nodes, then we need local community detection.
Moreover, If the graph is directed one, just like citation networks, then there would be
lots of dierences. A new way of searching papers by using relative centrality on di-
rected graph as our local community detection method is provided. Modications of our
undirected version to directed version are also been made. Then we have two methods
of random walk, we are going to show that by using general type of random walk with
walking length under two steps is better than the rst type of random walk with walking
length in single step. After our experiment, we can nd a larger size of community and
we believe our ranking order has more sense compared to only considering citation size,
because we take triangle into consideration, which means that our prior adding nodes
not only have direct link to the community but also have some two steps of links to the
community. Finally, we list some problems for our future works.

Contents 1
List of Figures 2
1 Introduction 3
2 The Framework 6
2.1 Brief Review of Undirected Model . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Fixed Model on Directed Networks . . . . . . . . . . . . . . . . . . . . . 9
3 Local Community Detection on Citation Networks 13
3.1 Random Walk on Directed Networks . . . . . . . . . . . . . . . . . . . . 13
3.2 Properties of Citation Networks . . . . . . . . . . . . . . . . . . . . . . . 18
3.3 Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4 Experiment 20
4.1 Experiment Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5 Conclusion 27

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