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# 数学代写|图论代写Graph Theory代考|Social networks

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## 数学代写|图论代写Graph Theory代考|Online communities

In their landmark essay, Licklider and Taylor [1968] foresaw that computers would form a major communication device between people leading to the online communities much like the ones we know today. Indeed, perhaps one of the biggest successes of the Internet has been the ability to allow people to exchange information with each other by means of user-to-user messaging systems [Wams and van Steen, 2004]. The best known of these systems is e-mail, which has been around ever since the Internet came to life. Another well-known example is network news, through which users can post messages at electronic bulletin boards, and to which others may subsequently react, leading to discussion threads of all sorts and lengths. More recently instant messaging systems have become popular, allowing users to directly and interactively exchange messages with each other, possibly enhanced with information on various states of presence.

It is interesting to observe that from a technological point of view, most of these systems are really not that sophisticated and are still built with technology that has been around for decades. In many ways, these systems are simple, and have stayed simple, which allowed them to scale to sizes that are difficult to imagine. For example, it has been estimated that in 2006 almost 2 million e-mail messages were sent every second, by a total of more than 1 billion users. Admittedly, more than $70 \%$ of these messages were spam or contained viruses, but even then it is obvious that a lot of online communication took place. These numbers continue to rise.

More than the technology, it is interesting to see what these communication facilities do to the people who use them. What we are witnessing today is the rise of online communities in which people who have never met each other physically are sharing ideas, opinions, feelings, and so on. In fact, Dodds et al. [2003] have shown that also for online communities we are dealing with what is known as a small world. To put it simply, a small world is characterized by the fact that every two people can reach each other through a chain of just a handful of messages. This phenomenon is also known as the “six degrees of separation” [Watts, 2003] to which we will return extensively later.

Dodds et al. were interested to see whether e-mail users were capable of sending a message to a specific person without knowing that person’s address. In that case, the only thing you can do is send the message to one of your acquaintances, hoping that he or she is “closer” to the target than you are. With over 60,000 users participating in the experiment, they found that 384 out of the approximately 24,000 message chains made it to designated target people (there were 18 targets from 13 different countries all over the world). Of these 384 chains, $50 \%$ had a length smaller than $5-7$, depending on whether the target was located in the same country as where the chain started.

What we have just described is the phenomenon of messages traveling through a network of e-mail users. Users are linked by virtue of knowing each other, and the resulting network exhibits properties of small worlds, effectively connecting every person to the others through relatively small chains of such links. Describing and characterizing these and other networks forms the essence of network science.

Long before the Internet started to play a role in many people’s lives, sociologists and other researchers from the humanities have been looking at the structure of groups of people. In most cases, relatively small groups were considered, necessarily because analysis of large groups was often not feasible.

An important contribution to social network analysis came from Jacob Moreno who introduced sociograms in the 1930s. A sociogram can be seen as a graphical representation of a network: people are represented by dots (called vertices) and their relationships by lines connecting those dots (called edges). An example we will come across in Chapter 9 is one in which a class of children are asked who they like and dislike. It is not hard to imagine that we can use a graphical representation to represent who likes whom, as shown in Figure 1.3.

Decades later, under the influence of mathematicians, sociograms and such were formalized into graphs, our central object of study. As mentioned, graphs are mathematical objects, and as such they come along with a theoretical framework that allows researchers to focus on the structure of networks in order to make statements about the behavior of an entire social group.

Social network analysis has been important for the further development of graph theory, for example with respect to introducing metrics for identifying importance of people or groups. For example, a person having many connections to other people may be considered relatively important. Likewise, a person at the center of a network would seem to be more influential than someone at the edge. What graph theory provides us are the tools to formally describe what we mean by relatively important, or having more influence. Moreover, using graph theory we can easily come up with alternatives for describing importance and such. Having such tools has also facilitated being more precise in statements regarding the position or role that person has within a community.

## 数学代写|图论代写GRAPH THEORY代考|ONLINE COMMUNITIES

Jacob Moreno 对社交网络分析做出了重要贡献，他在 1930 年代引入了社会图。社会图可以看作是网络的图形表示：人用点表示C一种ll和d在和r吨一世C和s以及它们的关系通过连接这些点的线C一种ll和d和dG和s. 我们将在第 9 章遇到的一个例子是，一个班级的孩子被问到他们喜欢和不喜欢谁。不难想象，我们可以用图形表示来表示谁喜欢谁，如图 1.3 所示。

## Matlab代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。