Question: Consider the following model to generate random graphs. Start with one single node. At each time step, to every node of the network either zero,

Consider the following model to generate random graphs. Start with one single node. At each time step, to every node of the network either zero, one or two new nodes are connected by means of a single link with probability 0 = 0.1, 1 = 0.3 and 2 = 0.6, respectively. If at any time step no node gains a new neighbour, the algorithm stops. a) Starting with one single node, what is the probability that a network with only 3 nodes is generated? Explain step by step your answer by describing all possibilities of how this could happen in each time step.

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 Mathematics Questions!

Describe how to construct the function cpo ((D E), v) of two cpos (D, vD) and (E, vE). Prove that ((D E), v) is a cpo. (You may use facts about least upper bounds provided you state them clearly.)...

Please summarize below. ILLUSTRATION: FROM SUPERSTORMS TO FACTORY FIRES MANAGING UNPREDICTABLE SUPPLY-CHAIN DISRUPTIONS BY DAVID SIMCHI-LEVI, WILLIAM SCHMIDT, AND YEHUA WEI TRADITIONAL METHODS FOR...

Scenario [Slide 34] Part 2: "Do" the Blockchain Activity [Slides 33-53] We are creating a blockchain to develop a distributed ledger to track the sales of a candy bar known as "CB1." Our company...

Consider the following model to grow simple networks. At time t = 1 we start with a complete network with n 0 = 6 nodes. At each time step t > 1 a new node is added to the network. The node arrives...

Python and most Python libraries are free to download or use, though many users use Python through a paid service. Paid services help IT organizations manage the risks associated with the use of...

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...

Write an alternative definition that is tail-recursive (iterative) and makes use of accumulator variables. [10 marks] Explain why your alternative definition executes more efficiently. [3 marks] 1...

can someone solve this Modern workstations typically have memory systems that incorporate two or three levels of caching. Explain why they are designed like this. [4 marks] In order to investigate...

(i) Write down the linear program relaxation for the vertex cover problem and solve the linear program. [6 marks] (ii) Based on the solution of the linear program in (b)(i), derive an integer...

s1 educated (SSE) student for every three public school educated (PSE) students. Reasoning that students are not very dissimilar from threads, he suggests the following entry and exit routines be...

Watch the Sarbanes-Oxley, Ten Years Later discussion, presented by the Center for Audit Quality (CAQ), to mark the 10th anniversary of the laws passage at New York Ideas. Discuss how the...

The following information was taken from Lamberson Company's accounting records: Account Balances January 1, December 31, Account Titles 2016 2016 Debits Cash S1.400 $2,400 Accounts Receivable (net)...

Calculate the midpoint of the line segment between a (5, 2) and (2, 6) b (4, 5) and (3, 0) c (7, 5) and (10, 10).

A company issues 1,050 shares of its common stock for $33,600 cash. Prepare journal entries to record this event under each of the following separate situations.