# 统计代写|网络分析代写Network Analysis代考|CSCl5352

## 统计代写|网络分析代写Network Analysis代考|Complex graphs

Over the past few decades, large real-world systems, such as WWW, Internet, social networks, wireless networks, supply-chain networks, are often modeled as a graph for the ease of computational analysis. The interaction relationships across different entities or macromolecules in the biological systems, such as protein-protein interactions (PPI), gene regulation and association, signaling pathways, metabolic activities, neuronal connectivity of a brain, etc., are also modeled as graphs or networks. However, such graphs are not simple graphs as regular graphs. Due to their unconventional topological properties, they are often treated as complex graphs or networks. Unlike conventional graphs, realworld networks exhibit non-trivial topological properties, such as varying degree distributions, high or low clustering coefficients, degree assortativity or average path length of the network. Accordingly, networks are classified into different models.

Before discussing various network models, it is important to understand the topological characteristics of any complex network. Usually, network models are defined based on such characteristics only. Thus we discuss topological characteristics first before introducing available models.

In a network, the interconnection patterns among the nodes are termed as network topology. The varying topological properties of any complex networks make the task of network comparison and classification a challenging activity. Therefore a set of summary statistics or quantitative performance measures are important to describe and compare the complex networks. In the last few years, many quantities and measures are proposed and investigated for complex network analysis. However, among all, three measures, namely average path length $(L)$ [2], clustering coefficient (Cc) $[16,33]$, and degree distribution $\left(P_k\right)[1,3]$ play a key role in complex network analysis. Next, we discuss different topological characteristics considered for any complex networks.

## 统计代写|网络分析代写Network Analysis代考|Rich club coefficient

The rich-club coefficient, introduced by Zhou and Mondragon in the context of the Internet topology [36], refers to the tendency of high-degree nodes (i.e., the hubs) in the network, to be very well-connected to other hub nodes. The name “rich-club” arises from the metaphor that the nodes with a large number of links, i.e., the hubs are “rich”, and they tend to be tightly and wellinterconnected between themselves, forming subgraphs called “club”. The rich-club coefficient is nothing but the measure of connectedness density within the club. A network with a rich club organization is shown in Fig. $4.4$ for better understanding.

The nodes in a network can be categorized by a ranking scheme [36] or by their degree [8]. The rank $r$ of a node represents the corresponding position of the node in the list of descending order of node degrees, i.e., the most highly-connected node is ranked as $r=1$, the second best-connected node is $r=2$, and so on. The density of connections between the $r$ richest nodes is evaluated by the rich-club coefficient [36],
$$\Phi(r)=\frac{2 E(r)}{r(r-1)},$$
where $E(r)$ is the total number of links between $r$ hub nodes and $r(r-1) / 2$ is the maximum possible number of links among these nodes. Similarly, the rich-club coefficient [8] in terms of node de-gree can be represented as follows:
$$\Phi(k)=\frac{2 E_k}{N_k\left(N_k-1\right)},$$
where $E_k$ is the number of links present between the nodes of degree greater than or equal to $k$, and $N_k$ is the number of such nodes. Therefore, $\Phi(k)$ measures the fraction of actual links connecting those nodes and the maximum number of possible links. This measure explicitly reflects how densely connected are the nodes within a network.

The behavior of the rich-club coefficient is proportional to the value of $k$. It means, a rich-club coefficient increasing with the degree $k$ indicates that there exists a rich-club of nodes, which are densely interconnected than the nodes with smaller degrees. Contrarily, a decrease in the value of $\Phi(k)$ indicates the presence of many loosely connected and relatively independent subgroups. It is known as rich-club phenomenon.

## 统计代写|网络分析代写Network Analysis代考|Rich club coefficient

$$\Phi(r)=\frac{2 E(r)}{r(r-1)},$$

$$\Phi(k)=\frac{2 E_k}{N_k\left(N_k-1\right)},$$

Rich-club 系数的行为与 $k$. 这意味着，一个rich-club系数随着度数的增加而增加 $k$ 表示存在丰富的节点倶乐 部，与度数较小的节点相比，这些节点之间的互连更密集。反之，价值下降 $\Phi(k)$ 表示存在许多松散连接且 相对独立的子群。它被称为富人倶乐部现象。

myassignments-help数学代考价格说明

1、客户需提供物理代考的网址，相关账户，以及课程名称，Textbook等相关资料~客服会根据作业数量和持续时间给您定价~使收费透明，让您清楚的知道您的钱花在什么地方。

2、数学代写一般每篇报价约为600—1000rmb，费用根据持续时间、周作业量、成绩要求有所浮动(持续时间越长约便宜、周作业量越多约贵、成绩要求越高越贵)，报价后价格觉得合适，可以先付一周的款，我们帮你试做，满意后再继续，遇到Fail全额退款。

3、myassignments-help公司所有MATH作业代写服务支持付半款，全款，周付款，周付款一方面方便大家查阅自己的分数，一方面也方便大家资金周转，注意:每周固定周一时先预付下周的定金，不付定金不予继续做。物理代写一次性付清打9.5折。

Math作业代写、数学代写常见问题

myassignments-help擅长领域包含但不是全部:

myassignments-help服务请添加我们官网的客服或者微信/QQ，我们的服务覆盖：Assignment代写、Business商科代写、CS代考、Economics经济学代写、Essay代写、Finance金融代写、Math数学代写、report代写、R语言代考、Statistics统计学代写、物理代考、作业代写、加拿大代考、加拿大统计代写、北美代写、北美作业代写、北美统计代考、商科Essay代写、商科代考、数学代考、数学代写、数学作业代写、physics作业代写、物理代写、数据分析代写、新西兰代写、澳洲Essay代写、澳洲代写、澳洲作业代写、澳洲统计代写、澳洲金融代写、留学生课业指导、经济代写、统计代写、统计作业代写、美国Essay代写、美国代考、美国数学代写、美国统计代写、英国Essay代写、英国代考、英国作业代写、英国数学代写、英国统计代写、英国金融代写、论文代写、金融代考、金融作业代写。

Scroll to Top