Graphs (Network)

# Graphs (Network) - A B C D E A F T T F F B T F F F T C T F...

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Unformatted text preview: A B C D E A F T T F F B T F F F T C T F F T F D F F T F T E F T F T F 2D array 5x5 ○ Boolean matrix ○ Boolean[ ][ ] M=new boolean [5][5] ○ Adjacency matrix/table storage 1. need int or float matix ○ True=> edge weight ○ False=> -1 ○ Weighted/Directed graph 2. Storing a graph in a program O(n 2 ) ○ For graph with n vertices and e edges • Space? Is M[x][y] true? ○ Worst case time for adjacency matrix= O(1) • Is there an edge (x,y) [undirected graph] in the graph? Worst case time= O(n) • Best case time= O(n) • Scan row x • What are all the neighbors of x? Max # of edges= n(n-1) • 2 Simple graph with n verticies O(n logn)= dividing line • Dense vs Sparse Graphs Space: O(n 2 ) ○ O(1) □ Is edge (x,y) in graph? O(n) □ Find/List all neighbors of x Run time ○ Appropriate for dense graphs ○ For sparse graphs, waste a lot of space storing false values ○ Instead, store the neighbors for each of the vertices in a LL ○ Adjacency matrix 1. n+2e # of array spots=n 2e undirected □ E directed □ # of nodes= O(n+e) Space: ○ Is edge (x,y) in graph? Run time: ○ Adjacency LL 2. Storage Schemes A 0 C 2 B 1 D 3 E 4 Graphs (Network) Monday, April 04, 2011 3:49 PM Lecture Notes Page 1 O(min(n,e)) □ O(min(n,e)) □ Find/List all neighbors of x Much better for sparse graphs (generally considered default since graphs are usually more sparse) ○ O(1) Vertex num->name ○ Sequential search □ Worst case O(n) Vertex name-> num ○ Arrays 1....
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Graphs (Network) - A B C D E A F T T F F B T F F F T C T F...

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