Statistics-lab™可以为您提供uh.edu MATH4364 Network Analysis网络分析课程的代写代考和辅导服务！
MATH4364 Network Analysis课程简介
Network Analysis has become a widely adopted method for studying the interactions between social agents, information and infrastructures. The strong demand for expertise in network analysis has been fueled by the widespread acknowledgement that everything is connected and the popularity of social networking services. This interdisciplinary course introduces students to fundamental theories, concepts, methods and applications of network analysis in a practical manner. Students learn and practice hands-on skills in collecting, analyzing and visualizing network data.
PREREQUISITES
Understand fundamental concepts and theories from the fields of social network analysis and network science.
Apply this knowledge to solve real-world, network-centric problems.
Use basic and advanced analysis methods and tools to visualize and analyze network data.
MATH4364 Network Analysis HELP（EXAM HELP， ONLINE TUTOR）
Theorem 2.3.2. The maximum of number of nodes in a binary of height $k$ is $2^{k+1}-1$.
Proof. A tree with height $k$ contains $k-1$ level (root at level 0 ). ByTheorem 2.3.1, the maximum number of nodes at level $L$ is $2^L$. Therefore, maximum number of nodes in a tree of height $k$ is the sum of the geometric series.
$$
N=\sum_{L=0}^{k-1} 2^L=\frac{2^{k+1}-1}{2-1}=2^{k+1}-1
$$
Theorem 2.3.3. If $N$ be the total number of nodes, then the height of the tree is at most $N-1$ and at least $\left\lceil\log _2 N\right\rceil$.
Proof. In case of extreme skewed tree each level contains one node. Therefore, the height of the tree become $N-1$ (root at 0 level).
However, in case of perfect binary tree of height $k$, the maximum number of nodes (Theorem 2.3.2) is
$$
\begin{aligned}
N & =2^{k+1}-1 \
k+1 & =\log _2 N+1
\end{aligned}
$$
therefore, $k=\left\lceil\log _2 N\right\rceil$
Textbooks
• An Introduction to Stochastic Modeling, Fourth Edition by Pinsky and Karlin (freely
available through the university library here)
• Essentials of Stochastic Processes, Third Edition by Durrett (freely available through
the university library here)
To reiterate, the textbooks are freely available through the university library. Note that
you must be connected to the university Wi-Fi or VPN to access the ebooks from the library
links. Furthermore, the library links take some time to populate, so do not be alarmed if
the webpage looks bare for a few seconds.
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