### 统计代写|网络分析代写Network Analysis代考|ESS2022

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

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

The sequential representation of a graph using an array data structure uses a two-dimensional array or matrix called adjacency matrix.

Definition 2.2.1 (Adjacency matrix). Given a graph $\mathcal{G}=(\mathcal{V}, \mathcal{E})$, an adjacency matrix, say $A d j$ is a square matrix of size $|\mathcal{V}| \times|\mathcal{V}|$. Each cell of $A d j$ indicates an edge between any two vertices or nodes:
$$A d j[i][j]= \begin{cases}\omega, & \text { if }\left(v_i, v_j\right) \in \mathcal{G}(\mathcal{E}) \ 0, & \text { otherwise }\end{cases}$$
where $\omega$ is the weight of the edge between the nodes $v_i$ and $v_j$. In the case of an unweighted graph, $\omega$ is considered as 1, whereas for weighted graph it may be any value according to the problem in hand. See Fig. 2.10.

Adjacency matrices of undirected graphs are symmetric, where $A d j[i][j]=A d j[j][i]$, for $i, j$. In other words, we may say that $A d j$ and its transpose $A d j^{\prime}$ is the same. Unlike undirected graph, digraph produces asymmetric matrix.
Finding degree of a node
One of the important operations on a graph is finding the degree of a given node. From the adjacency matrix, it is easy to determine the connection of any nodes. The degree of a node in an undirected graph can be calculated as follows:
$$\operatorname{deg}\left(v_i\right)=\sum_{j=1}^n A d j[i][j],$$

where values in the $i^{t h}$ row in the adjacency matrix indicates the connections to $n$ different nodes from the node $i$ in the graph. Similarly, in the case of digraph, the indegree and outdegree of a node can be calculated as follows:
$$\text { indeg }\left(v_i\right)=\sum_{j=1}^n \operatorname{Adj}[j][i] \text { and outdeg }\left(v_i\right)=\sum_{j=1}^n \operatorname{Adj}[i][j] \text {. }$$

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

Array data structures are easy to access and fast in traversing. However, for a large graph, it is not always feasible to use adjacency matrix representation, due to large memory requirements. It is even more ineffective if a graph contains more nodes with relatively few connections or edges (sparse graph); this leads to the formation of a sparse matrix. To overcome such situation, list representation is an effective alternative for memory representation of large and dense graphs. An advantage of list representation is that it can be used for dynamic graphs, where vertices and edges are growing and shrinking with time. It is commonly implemented in any programming languages as an array of a singly-linked list. The size of the array is the number of vertices in the graph. Each singly linked list keeps track of the neighbors of a vertex. In the case of a weighted graph, the weights of an edge between a pair of vertices are stored in the nodes of singly-linked list itself as a separate entry together with vertex level. It is easy to calculate the degree of a vertex by looking into the number of nodes in the list of the vertex. For example, the degree of the vertex $\mathbf{C}$, which is four (04), can easily be calculated by finding the length of the list headed by $\mathrm{C}$, as given in Fig. $2.11$.

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

$$\operatorname{Adj}[i][j]=\left{\omega, \quad \text { if }\left(v_i, v_j\right) \in \mathcal{G}(\mathcal{E}) 0, \quad\right. \text { otherwise }$$

$$\operatorname{deg}\left(v_i\right)=\sum_{j=1}^n \operatorname{Adj}[i][j],$$

$$\operatorname{indeg}\left(v_i\right)=\sum_{j=1}^n \operatorname{Adj}[j][i] \text { and outdeg }\left(v_i\right)=\sum_{j=1}^n \operatorname{Adj}[i][j] \text {. }$$

## 有限元方法代写

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## 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。