3. Use the Network in Figure-3 and answer the following questions (a - d).ABEDGFFigure 3Find the Clustering Co-efficient of node A and C.b. Which edge(s) have smallest neighborhood overlap?Find the embeddedness of edge ED and BC.d. Find the betweenness of edge AB and FG.а.С.

a) clustering coefficient is a measure of the degree to which nodes in a graph tend to cluster…

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Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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b. Illustrate the working of depth first search for the given graph, to find all nodes reachable from A В Н. E F H. J I
Problem 3 1) Consider that you have a graph with 8 vertices numbered A to H, and the following edges: (A, B), (A, C), (B, C), (B, D), (C, D), (C, E), (D, E), (D, F), (E, G), (F, G), (F, H), (G, H) a) Using depth-first search algorithm, what would be the sequence of visited nodes starting at A (show the content of the stack at some steps). b) Same question if the algorithm used in breadth first search. c) What would be the minimum spanning tree rooted at A if a Depth First Search algorithm is used (refer to question a), show few steps in running the algorithm. d) What would be the minimum spanning tree if a Breadth First Search algorithm is used (refer to question b), show few steps of the algorithm.
(d) Let G = (V, E) be the connected, directed graph below, with edge failure probabili- ties given on each edge. Edges fail independently of each other. A .5 B Compute the probability that the failed edges disconnect A from B.
a. Show that K6.7 has a path containing all vertices in the graph. b. Explain why K6,7 is not Hamiltonian.
question 5. Draw an Eulerian graph and a Hamiltonian graph, both of more than four vertices.
Determine whether the graph is bipartite. u V y W X
a) Find adjacency matrix/edge endpoint function for the graph given below. Also find a circuit of length 7 if possible and draw graphically.
1. For each pair of vertex in no. 3 give the vertex sequence of the longest path connecting them that repeat no edges. Is there a longest path connecting them? 2. How many spanning trees are can be generated from its graph? Define 2 spanning trees of Graph A and B. 3. Which graph has and Euler path? Euler Circuit? (Use Fleury’s Algorithm) For those that don’t give an explanation? 4. Which graph contains Hamiltonian Path? Hamiltonian Circuit? For those that don’t give an explanation?
5. Let G = (V,E) be a loop-free connected unicyclic graph (contains one single cycle).If G has five vertices of degree 2, two vertices of degree 3, and three vertices of degree 4, howmany pendant vertices (leaves) does it have. (Assuming that maximum degree in G is 4).
1
8. (a) Find the chromatic number x of the 9-vertex graph below. Explain. (b) Find the edge chromatic number x' of the graph below. Explain. А B D O F E I H. (c) Does this graph have a Hamiltonian cycle? If so, list the vertices in order of such cycle. If not, explain why not. (d) Does this graph have an Euler circuit? If so, explain how you know. If not, does it have an Euler path? If so, explain how you know. Include a drawing of this graph in your solution.
Determine the vertex- and edge-connectivity of the given graph and explain why.

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Find the Clustering Co-efficient of node A and C. b. Which edge(s) have smallest neighborhood overlap? c. Find the embeddedness of edge ED and BC. d. Find the betweenness of edge AB and FG. а.