# Let G be a connected undirected graph with N nodes and L links. For each i {1, .

Let G be a connected undirected graph with N nodes and L links. For each i ∈ {1, . . . , N} define di as the degree of nodei, being the number of links it is attached to. We take a random walk over the graph according to the following CTMC: Whenwe visit a new node i, we stay there for an independent and exponentially distributed time with rate vi. We then choose tovisit a new node j independently and uniformly over all neighboring nodes.a) Make a guess about the steady state distribution for each state i ∈ {1, . . . , N} in terms of di and vi.b) Verify your guess with the detail equations.c) For the same graph, consider a discrete time Markov chain (DTMC) where, every slot t, we move to a new nodeindependently and uniformly over all neighboring nodes. Show that the discrete time detail equations πiPij = πjPji aresatisfied for a particular guess probably mass function πi for i ∈ {1, . . . , N}.d) Consider the following modification to the DTMC in part (c): We transition according to the same DTMC. However,we stay in each state i for an independent random amount of time that has a general distribution with mean E [Ti]. It canbe shown that the fraction of time in each state i is proportional to πiE [Ti], where πiis the steady state distribution of thediscrete time chain. Verify this is true for the special case when Tiis exponentially distributed with rate µi. It follows that thesteady state results for the CTMC in part (b) are the same even if the time in each state is not exponentially distributed

Don't use plagiarized sources. Get Your Custom Essay on
Let G be a connected undirected graph with N nodes and L links. For each i {1, .
Just from \$13/Page

## Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
\$26
The price is based on these factors:
Number of pages
Urgency
Basic features
• Free title page and bibliography
• Unlimited revisions
• Plagiarism-free guarantee
• Money-back guarantee
On-demand options
• Writer’s samples
• Part-by-part delivery
• Overnight delivery
• Copies of used sources
Paper format
• 275 words per page
• 12 pt Arial/Times New Roman
• Double line spacing
• Any citation style (APA, MLA, Chicago/Turabian, Harvard)

# Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

### Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

### Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

### Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.