Question: [Python and Sage Question] All computations should use the SageMath 9.0 kernel. However, you are free to mix Python and Sage functionality in your code.

[Python and Sage Question]

All computations should use the SageMath 9.0 kernel. However, you are free to mix Python and Sage functionality in your code.

[Python and Sage Question] All computations should use the SageMath 9.0 kernel.

Problem 2: Diameters of random graphs Grading criteria: code correctness for a; soundness of methodology and thoroughness for b and c. a. Let G be a graph on n vertices. We say that G is compact if any two vertices are connected by a path of length at most log2 n. Write a Python function to test whether a given graph is compact. In [ ]: b. For pe [0,1], consider a graph on n = 100 vertices in which each pair of vertices is joined by an edge with probability p (uniformly at random). Estimate the minimum value of p for which the probability that the resulting graph is compact exceeds 1/2. Justify your guess with some numerical evidence. In [ ]: C. For m a positive integer, consider a graph on n = 100 vertices with exactly m edges, chosen uniformly at random from all graphs with these properties. Estimate the minimum value of m for which the 21 probability that the resulting graph is compact exceeds 1/2. Justify your guess with some numerical evidence. Problem 2: Diameters of random graphs Grading criteria: code correctness for a; soundness of methodology and thoroughness for b and c. a. Let G be a graph on n vertices. We say that G is compact if any two vertices are connected by a path of length at most log2 n. Write a Python function to test whether a given graph is compact. In [ ]: b. For pe [0,1], consider a graph on n = 100 vertices in which each pair of vertices is joined by an edge with probability p (uniformly at random). Estimate the minimum value of p for which the probability that the resulting graph is compact exceeds 1/2. Justify your guess with some numerical evidence. In [ ]: C. For m a positive integer, consider a graph on n = 100 vertices with exactly m edges, chosen uniformly at random from all graphs with these properties. Estimate the minimum value of m for which the 21 probability that the resulting graph is compact exceeds 1/2. Justify your guess with some numerical evidence

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

[Python and Sage Question] All computations should use the SageMath 9.0 kernel. However, you are free to mix Python and Sage functionality in your code. Problem 3: Connectivity in an electrical...

[Python and Sage Question] All computations should use the SageMath 9.0 kernel. However, you are free to mix Python and Sage functionality in your code. Problem 4: Network data from a CSV file...

[Python and Sage Question] All computations should use the SageMath 9.0 kernel. However, you are free to mix Python and Sage functionality in your code. Problem 1: Super Bowl LIV [ Edit Grading...

[Python and Sage Question] All computations should use the SageMath 9.0 kernel. However, you are free to mix Python and Sage functionality in your code. Problem 5: Modeling the Internet graph Grading...

NOTE: If You read through the question carefully all the material needed for this question are provided. In exercise 11.2.3 : ( The Exercise in Question is the one below this question. (EXERCISE:...

NOTE: The material referenced by the question is below the question. ALGEBRAIC STRUCTURES: DISCRETE MATH In exercise 11.2.3 : i. Items (b), (d), (e), and (f) are groups. For each, show what the...

ALGEBRAIC STRUCTURES: DISCRETE MATH In exercise 11.2.3 : i. Items (b), (d), (e), and (f) are groups. For each, show what the identity is, and what the inverse of atypical element is. ii. Item (a) is...

A ( n ) _ _ _ _ _ _ _ _ _ _ is an unordered collection of items with no duplicates. Question 1 options: dictionary file set tuple Question 2 ( 1 point ) Elements of a set are delimited with _ _ _ _ _...

I need help answering questions 3 to 9. using python please! jupyterhub.egr.msu.edu anthrokids su. HW-02 Anthr... numpy.loadtxt Part 2: Workin... Day-08 Pra-C... Day-08 Pre-c.. Day-07 In-Cla.. Python...

Question 1 0.25 pts The following code is used to retrieve help information about a python function called type) 1 help type). Which of the following statements is NOT true? You can call a function...

In many UNIX systems, the i-nodes are kept at the start of the disk. An alternative design is to allocate an i-node when a file is created and put the i-node at the start of the first block of the...

Use the parallel-axis theorem to show that the moments of inertia given in parts (a) and (b) of Table 9.2 are consistent.

If the coupon rate on a bond is 4 . 5 % and the bond is selling at a discount, which of the following is the most likely yield to maturity on the bond? 4 . 2 % 4 . 3 % 3 . 8 % 5 . 2 %

Johnny Cake Limited has 8 million shares of stock outstanding selling at $22 per share and an issue of $40 million in 10 percent annual coupon bonds with a maturity of 17 years, selling at 94.0...

2. Identify the purpose of your speech

5. Cull from among your sources the material that will be most convincing

4. In this chapter, we talked about some of the challenges that todays organizations face, including worklife balance, sexual harassment, and communication technology. Does your organizationbe it a...