網路中謠言散播中心的研究

Abstract

在現今的世界裡，互連的網路結構中充滿著風險：一個單點發生問題， 可能因為互連的結構而被傳播至整個網路，進而放大其負面影響。從本質 上來看，可以用謠言在網路中傳播的模型，來描述這種形式的傳播，在有 傳播的模型之後，我們進一步的希望可以找到問題的源頭，並且在有限的 資訊下(只知道有問題的點的互連關係)，加以控制以及預防這類型的風險 發生。 在這篇論文當中，我們以樹狀網路為主，利用從著名的傳染病模 型SIR-模型"簡化而來的謠言散佈模型"來研究問題的源頭可能出現在 哪裡。這篇論文將會包含一些有限樹狀網路與無限樹狀網路的新結果。

In the modern world there are many network risks which share a common structure: an isolated risk is amplified because it is spread by the network. In essence, all of these types of spreading phenomenon can be modeled as a rumor spreading through a network, where the goal is to find the source of the rumor in order to control and prevent these network risks based on limited information about the network structure and the rumor infected nodes. In this thesis, we shall use the so-called Rumor Spread model which is simplified from an epidemic model called Susceptible-Infected-Recovered model to study the Rumor Center in a tree-shaped network. Several new results are obtained on the cases where the network is defined on a d-regular tree either infinite or finite.