有許多的現象像流行病一樣擴散，例如病毒傳染丶謠言丶意試型態丶產品行銷等
等。當在網路中出現兩個競爭者時，便出現了一個疑問：佔據一開始的哪些位置
能影響到最多的人。我們將兩種病毒在網路中擴散的模型稱為 SI1I2 model。從
一種病毒延伸到兩種病毒時，在數學近似上出現了一些問題。我們根據社群偵測
的結果導出一個合適的數學近似方程式。比較了幾種一開始選擇位置的策略。選
擇每個社群中選擇網路中鄰居最多的點會能有較大的影響力。數學的近似也支持
這個結果。

Many phenomena can be model as epidemic in social network, such as viruses, rumors,ideologies, or marketing etc. When there exist two competitors who try to maximize
each spread in the network, there comes the question that what nodes target in the very beginning to achieve the maximum spread. The epidemic model we use is called
SI1I2(Susceptible-Infected1-Infected2) model, where there are two viruses spreading in the network. We find that there are some problems when extending the approximation from one virus to two viruses. We derive the appropriate approximation according to community detection result. We compare several strategies for the initial chosen nodes
for each competitor. Choosing top degree nodes in each community is the strategy we give which has more influence than others according to centrality properties. Our
approximation agrees with these results.

Contents 1
List of Figures 3
1 Introduction 4
2 Model 6
2.1 SI1I2 model 6
2.2 Community detection 7
3 Approximation 8
3.1 Mean-eld approximation 8
3.2 Degree-based approximation 10
3.3 Degree-based approximation with communities 12
4 Experiments 15
5 Conclusions 22
Bibliography 23

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