A graph with n nodes is created by randomly connecting some pairs of nodes by edges If the connection probability per pair is p, then all pairs from a triple of nodes are connected with probability p3 For p small and n 3 p3 moderate in size, the number of such triangles in the random graph is approximately Poisson with mean Use the neighborhood method to estimate the total variation error in this approximation

The Answer is in the image, click to view ...

Question: A graph with n nodes is created by randomly connecting some pairs of nodes by edges. If the connection probability per pair is p, then

A graph with n nodes is created by randomly connecting some pairs of nodes by edges. If the connection probability per pair is p, then all pairs from a triple of nodes are connected with probability p3. For p small and λ = n 3

p3 moderate in size, the number of such triangles in the random graph is approximately Poisson with mean λ. Use the neighborhood method to estimate the total variation error in this approximation.

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 Probability And Stochastic Modeling Questions!

=+8. A graph with n nodes is created by randomly connecting some pairs of nodes by edges. If the connection probability per pair is p, then all pairs from a triple of nodes are connected with...

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

Consider a set of n people who are members of an online social network. Suppose that each pair of people are linked as friends independently with probability 1/2. We can think of their relationships...

Consider a set of n people who are members of an online social network. Suppose that each pair of people are linked as "friends" independently with probability 1/2. We can think of their...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

Consider the Markov Chain, Xn, on the states i = 0, 1, 2, . . . with transition matrix given by pi,i1 = p i = 1, 2, . . . pi,i+1 = 1 p i = 0, 1, . . . p0,0 = p where 0

Digital Electronics An arbiter is a functional unit that allows requesters to lock resources while they are in use. (a) Describe the inputs and outputs of an arbiter for a single resource which has...

Hello! Please answer Problem 2, and include any necessary classes from the previous question if they are needed. Thank you! Problem statement A Graph is formally define as G-N,E) consisting of the...

A creative engineer suggests structuring the TLB so that not all the bits of the presented address need match to result in a hit. Suggest how this might be achieved, and what might be the costs and...

Your clients, Tom and Teri Trendy, have a 20-year old son, Tim. Tim lives in Hawaii, where he studies the effects of various sunscreens on his ability to surf. Last year, Tim was out of money and...

Show that ?E/E the fractional loss of energy of a photon during a collision with a particle of mass m, is given by where E is the energy of the incident photon, f' is the frequency of the scattered...

Sarasota Inc. went public 3 years ago. The board of directors will be meeting shortly after the end of the year to decide on a dividend policy. In the past, growth has been financed primarily through...

In this exercise, assume that we are considering enhancing a machine by adding vector hardware to it. When a computation is run in vector mode on the vector hardware, it is 10 times faster than the...