This document discusses exercises on graph search algorithms using a social network graph as an example. It includes exercises on determining if the graph is directed or undirected, finding the most connected member, connected components, degrees of separation between members using breadth-first search, and finding all members within a given degree of separation. Students are instructed to complete methods for finding connected components, degrees of separation between two members, and finding all members within a given degree of separation from a starting member.

1. CompSci 201
Recitation 14
Graph search exercises
April 20, 2015
Austin Lu (Head UTA)
Professor Azhar

2. A Social Network Graph
CompSci 201
• Imagine a social network graph with members as
vertices, identified by some integer ID
• Assume connections are mutual
• Is this graph directed or undirected?
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3. Discussion
CompSci 201
• Snarf the code for today
• How is the graph represented?
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4. Discussion
CompSci 201
• Which member has the most connections?
• How do you find out in code?
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5. Discussion
CompSci 201
• What are the connected components in the graph?
• How do we find them programmatically?
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6. findConnectedComponents()
CompSci 201
• Complete the findConnectedComponents method,
which returns a Set<Set<Integer>> where each
element is a set of all members in a connected
component
• Why a set?
• Complete and use dfs(int start, Set<Integer> visited)
for this exercise
• Would breadth-first search also work?

7. Discussion
CompSci 201
• What should findConnectedComponents return on the
below graph (already created in main method)?
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8. Discussion
CompSci 201
• What should findConnectedComponents return on the
below graph (already created in main method)?
• {{0, 1, 2, 3, 4, 5, 6, 7, 11}, {8, 9, 10}}
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9. Degrees of separation
CompSci 201
• The “degree of separation” between two vertices is the
minimum number of nodes separating them
• E.g. starting from Member 0, the degree of separation to
• Member 0 (itself) => 0
• Members 1, 2, 3, 7 => 1
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10. Degrees of separation
CompSci 201
• E.g. starting from member 0, the degree of separation to
• Member 0 (itself) => 0
• Members 1, 2, 3, 7 => 1
• Members 4, 5, 6 => 2
• Member 11 => 3
• Members 8, 9, 10 (unreachable) => return -1
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11. Discussion
CompSci 201
• What should degreesOfSeparation(2, 4) return?
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12. Discussion
CompSci 201
• What should degreesOfSeparation(2, 4) return?
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13. Degrees of separation
CompSci 201
• Complete the method to return the degree of separation
between two members, int degreesOfSeparation(int from, int to)
• Which graph search is convenient to search by distance?
Breadth-first search
• Use a queue of Member(int id, int distance) objects to
keep track of both member id and degree of separation/distance
• As soon as you visit a member with ID == to, you can return the
distance immediately
• Remember to return -1 if the member to is unreachable

14. BFS
CompSci 201
• Recall: BFS pseudocode
bfs(start vertex s) {
- mark s as visited
- initialize Queue with s
- while (Queue is not empty):
- remove first node of Q, call it curr
- for each neighbor n of curr:
-if n is unvisited
-mark n as visited
-add n to Queue
}

15. findNthDegreeConnections
CompSci 201
• How might we modify a BFS to find all Nth degree connections?
• Complete the method
Set<Integer> findNthDegreeConnections(int from, int n)

16. Discussion
CompSci 201
• What should findNthDegreeConnections(4, 3) return?
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17. Discussion
CompSci 201
• What should findNthDegreeConnections(4, 3) return?
• {2, 3, 7, 11}
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18. To Do:
• Submit the recitation quiz before Monday 4/27, 3pm
• 2 allowed submissions, last score counts
• Optional relevant reading:
• Six degrees of separation theory
• Kevin Bacon number
• Happy last recitation!
Good luck on finals
CompSci 201