在這篇論文當中，我們使用一個網路生成模型來形成社群網路(Social network)。首先，我們以 個節點(Vertices)來形成一個完全連接(Fully-connected)的網路。在每一個時間點，都會有一個新的vertex加入到網路當中，然後它會在等機率的情況下，隨機挑選在前一個時間點時的網路中的任一個vertex與其連接。再來，被選中的那個vertex它所相鄰的節點(Neighbors)，會有一個機率a與該新加入的vertex形成連接。我們稱這個方法為”triadic attachment(TA)”。在進行我的研究之前，先前已經有先行做了一些網路分析，分別是平均節點分支度(mean degree)與群聚係數(clustering coefficient)。在這篇論文當中，我們依據前面所做的Model與分析過的數據。來去更進一步的探討在該網路模型上的Pearson Correlation Coefficient(皮爾遜積差相關係數)。

In this paper we derive a first-order linear differential equation
for the Pearson degree correlation function of a duplication model.
The solution of the differential equation shows that the degree
correlation coefficient function is negative at early times, but
tends to be positive at late times.

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