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Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is 1/2. What is the expected number of unordered cycles of length three?
- a)1/8
- b)1
- c)7
- d)8
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
Consider an undirected random graph of eight vertices. The probability...
A cycle of length 3 can be formed with 3 vertices. There can be total 8C3 ways to pick 3 vertices from 8. The probability that there is an edge between two vertices is 1/2. So expected number of unordered cycles of length 3 = (8C3)*(1/2)3 = 7
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Consider an undirected random graph of eight vertices. The probability...
Expected Number of Unordered Cycles of Length Three in a Random Graph
Understanding the Problem:
In an undirected random graph of eight vertices where the probability of an edge between any pair of vertices is 1/2, we need to find the expected number of unordered cycles of length three.
Solution Approach:
To find the expected number of unordered cycles of length three in the graph, we need to consider all possible sets of three vertices and calculate the probability of forming a cycle among them.
Calculating the Probability of Forming a Cycle:
- For a cycle of length three, we need three vertices connected in a cyclic manner.
- The probability of forming an edge between any two vertices is 1/2.
- Hence, the probability of forming a cycle among three vertices is (1/2) * (1/2) * (1/2) = 1/8.
Calculating the Expected Number of Cycles:
- There are a total of 8 choose 3 = 56 ways to select three vertices from eight.
- Each set of three vertices has a probability of 1/8 to form a cycle.
- Therefore, the expected number of cycles of length three can be calculated as 56 * 1/8 = 7.
Conclusion:
The expected number of unordered cycles of length three in the given random graph of eight vertices with a probability of 1/2 for any edge is 7.
Understanding the Problem:
In an undirected random graph of eight vertices where the probability of an edge between any pair of vertices is 1/2, we need to find the expected number of unordered cycles of length three.
Solution Approach:
To find the expected number of unordered cycles of length three in the graph, we need to consider all possible sets of three vertices and calculate the probability of forming a cycle among them.
Calculating the Probability of Forming a Cycle:
- For a cycle of length three, we need three vertices connected in a cyclic manner.
- The probability of forming an edge between any two vertices is 1/2.
- Hence, the probability of forming a cycle among three vertices is (1/2) * (1/2) * (1/2) = 1/8.
Calculating the Expected Number of Cycles:
- There are a total of 8 choose 3 = 56 ways to select three vertices from eight.
- Each set of three vertices has a probability of 1/8 to form a cycle.
- Therefore, the expected number of cycles of length three can be calculated as 56 * 1/8 = 7.
Conclusion:
The expected number of unordered cycles of length three in the given random graph of eight vertices with a probability of 1/2 for any edge is 7.
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Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is 1/2. What is the expected number of unordered cycles of length three?a)1/8b)1c)7d)8Correct answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is 1/2. What is the expected number of unordered cycles of length three?a)1/8b)1c)7d)8Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is 1/2. What is the expected number of unordered cycles of length three?a)1/8b)1c)7d)8Correct answer is option 'C'. Can you explain this answer?.
Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is 1/2. What is the expected number of unordered cycles of length three?a)1/8b)1c)7d)8Correct answer is option 'C'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is 1/2. What is the expected number of unordered cycles of length three?a)1/8b)1c)7d)8Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is 1/2. What is the expected number of unordered cycles of length three?a)1/8b)1c)7d)8Correct answer is option 'C'. Can you explain this answer?.
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Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is 1/2. What is the expected number of unordered cycles of length three?a)1/8b)1c)7d)8Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is 1/2. What is the expected number of unordered cycles of length three?a)1/8b)1c)7d)8Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Consider an undirected random graph of eight vertices. The probability that there is an edge between a pair of vertices is 1/2. What is the expected number of unordered cycles of length three?a)1/8b)1c)7d)8Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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