Given the following graph in Figure A1. < (1) (2 points) Find out the bridges and...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Given the following graph in Figure A1. < (1) (2 points) Find out the bridges and local bridges. < (2) (2 point) Find all the shortest paths between nodes B and F. < (3) (2 point) What is the diameter of the graph? (4) (2 points) Calculate the neighbourhood (edge) overlap values for edges (E, G). < ( 2 E D A F G C Figure. A1 B H Suppose we have the initial set S including six nodes in Figure A2. < (1) (2 points) we say that a node X is a local gatekeeper if there are two neighbors of X, say Y and Z, that are not connected by an edge. List all local gatekeepers in S. < (2) (4 points) If we add two nodes G and H to the network by BA algorithm with m=2, what's the probability that there is an edge between nodes G and H? H F A E B D C Figure. A24 new nodes G H 2 Given the following graph in Figure A3. < (1) (2 points) Calculate cluster coefficient values for nodes F. < (2) (2 points) Given a graph G, the dual construction can create a new graph G' based on the following rules: < (a) If (X, Y) is an edge of G, then XY is a node of G' (note that XY and YX are the same node in G'). < (b) If two edges in G share the same point, their corresponding nodes in G' are linked. More specifically, if edges (X, Y) and (X, Z) exist in G, nodes XY and XZ in G' are connected because they have a common point X in G. < Given the graph in Fig. A3, draw a new graph by applying the above dual construction. < (3) (2 points) Given a star with n edges (i.e., a central node and n leaf node linked with the central node, and n 2), what is the graph derived from the above dual construction? (notice that you do not need to draw your answer, just describe your answer) < C D F B Figure. A3+ E A (1) In a small-world network, how does the presence of a few highly connected nodes (hubs) influence the average path length, thus maintaining the small-world property? (2) . Are the graphs in Figure A4(2) isomorphic? If yes, show one possible one-to-one mapping between their nodes. < A B Loo D E 2 C 1 Figure. A4(2) < 4 2 5 6 3 Given the following graph in Figure B1. (1) (2 points) What are the nodes with the highest degree centrality? Explain your answer. < (2) (4 points) What are the nodes with the highest betweenness centrality? Explain your answer. < A D TI F B E Figure B1 H G Given the following graph in Figure A1. < (1) (2 points) Find out the bridges and local bridges. < (2) (2 point) Find all the shortest paths between nodes B and F. < (3) (2 point) What is the diameter of the graph? (4) (2 points) Calculate the neighbourhood (edge) overlap values for edges (E, G). < ( 2 E D A F G C Figure. A1 B H Suppose we have the initial set S including six nodes in Figure A2. < (1) (2 points) we say that a node X is a local gatekeeper if there are two neighbors of X, say Y and Z, that are not connected by an edge. List all local gatekeepers in S. < (2) (4 points) If we add two nodes G and H to the network by BA algorithm with m=2, what's the probability that there is an edge between nodes G and H? H F A E B D C Figure. A24 new nodes G H 2 Given the following graph in Figure A3. < (1) (2 points) Calculate cluster coefficient values for nodes F. < (2) (2 points) Given a graph G, the dual construction can create a new graph G' based on the following rules: < (a) If (X, Y) is an edge of G, then XY is a node of G' (note that XY and YX are the same node in G'). < (b) If two edges in G share the same point, their corresponding nodes in G' are linked. More specifically, if edges (X, Y) and (X, Z) exist in G, nodes XY and XZ in G' are connected because they have a common point X in G. < Given the graph in Fig. A3, draw a new graph by applying the above dual construction. < (3) (2 points) Given a star with n edges (i.e., a central node and n leaf node linked with the central node, and n 2), what is the graph derived from the above dual construction? (notice that you do not need to draw your answer, just describe your answer) < C D F B Figure. A3+ E A (1) In a small-world network, how does the presence of a few highly connected nodes (hubs) influence the average path length, thus maintaining the small-world property? (2) . Are the graphs in Figure A4(2) isomorphic? If yes, show one possible one-to-one mapping between their nodes. < A B Loo D E 2 C 1 Figure. A4(2) < 4 2 5 6 3 Given the following graph in Figure B1. (1) (2 points) What are the nodes with the highest degree centrality? Explain your answer. < (2) (4 points) What are the nodes with the highest betweenness centrality? Explain your answer. < A D TI F B E Figure B1 H G
Expert Answer:
Answer rating: 100% (QA)
Solution Bridges If there is an edge in the graph joining two nodes XY is a bridge if deleting the e... View the full answer
Related Book For
Fundamentals of Financial Management
ISBN: 978-0324664553
Concise 6th Edition
Authors: Eugene F. Brigham, Joel F. Houston
Posted Date:
Students also viewed these computer network questions
-
Creating a new product can be challenging for many companies, and there are a number of sources those ideas can come from. The company has access to its own internal sources for product ideas, but it...
-
A company cannot simply design product and marketing program and then set the price. Often, before the marketing program is set, the price is considered along with the other marketing mix variables....
-
What is the cooling load, expressed in btu/hr through this wall if the window is shaded, the indoor temperature is 75 F, and the outdoor temperature is 105 F
-
Let B > 0. Show that the maximum of subject to the constraints x + this to conclude that f(x,...,xn) = X1 X2 Xn for all positive numbers a,..., an. . + xn = B and xj 0 for j = 1,. n occurs for x =...
-
In an actual refrigeration cycle using R-12 as the working fluid, the refrigerant flow rate is 0.05 kg/s. Vapor enters the compressor at 150 kPa, 10C, and leaves at 1.2 MPa,...
-
Global or international recruitment is a straightforward process of hiring employees from anywhere and everywhere, without any geographical barriers. With the popularity of global recruitment,...
-
Farmer D. Jones has a crop of grapefruit that will be ready for harvest and sale as 150,000 pounds of grapefruit juice in 3 months. Jones is worried about possible price changes, so he is considering...
-
The Ski Factory provided the following information at December 31, 2015: Marketable Securities The company invested $52,000 in a portfolio of marketable securities on December 22, 2015. The...
-
The following selected data were taken from the accounting records of Colorado Enterprises: Month Manufacturing Overhead May June July August Machine Hours 50,500 61,800 $ 934,000 1,148,000 77,000...
-
Design a beam of ASTM A36 steel with allowable bending stress of 160 MPa to support the load shown in Figure P4-33. Assume a standard wide flange beam from Appendix F, or some other source can be...
-
Allocating Purchase Price Capri Holdings, the parent company of Michael Kors and Jimmy Choo, reports the following footnote to its 10-K report dated March 31, 2019. On December 31, 2018, the Company...
-
Derived demand is the demand for _________. a) final goods and services b) resources c) final goods as well as services and resources d) neither final goods and services nor resources.
-
When the demand for wheat rises, the demand for farm labor ________. a) rises b) falls c) may rise or fall
-
What is the difficulty in applying Gauss elimination to the following linear algebraic equations? \[ \begin{aligned} -5 x_{1}+5 x_{2} & =5 \\ 10 x_{1}-10 x_{2} & =-5 \end{aligned} \]
-
Automation will raise the level of employment if the _________. a) output effect is equal to the substitution effect b) output effect is greater than the substitution effect c) substitution effect is...
-
If Melissa produces twice as much per hour as Adam, we would say that she is ______________ as productive as he is.
-
For the reaction: 2N2O5(g) ? 4NO2(g) + O2(g) the rate law is:(?[O2]/?t) = k[N2O5] At 300 K, the half-life is 2.50 104 secondsand the activation energy is 103.3 kJ/mol. What is the half-life at310 K?...
-
g(x) = x 5 5x 6 a. Show that g(x) = 0 has a root, , between x = 1 and x = 2. b. Show that the equation g(x) = 0 can be written as x = (px + q) 1/r , where p, q and r are integers to be found. The...
-
Draw Project Ps NPV profile. Does Project P have normal or non-normal cash flows? Should this project be accepted? Explain.
-
Bowles Sporting Inc. is prepared to report the following income statement (shown in thousands of dollars) for the year 2009. Sales $15,200 Operating costs including depreciation 11,900 EBIT $ 3,300...
-
What are the four most fundamental factors that affect the cost of money, or the general level of interest rates, in the economy?
-
Explain the role of parameters and return values in exchanging messages.
-
Describe events. Provide an example.
-
What are the building blocks of a collaboration diagram?
Study smarter with the SolutionInn App