Graphs
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The document discusses different types of graphs including directed and undirected graphs. It describes graph implementations using adjacency matrices and adjacency lists. It also covers graph traversal algorithms like depth-first search (DFS) and breadth-first search (BFS). DFS prioritizes exploring paths as deeply as possible while BFS explores all paths at the same depth level before moving deeper. Real-world examples of graphs include social networks and transportation networks.
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Graphs
- 1. Graphs MADE BY Zulkifal Yousaf [email_address]
- 2. Graph A data structure that consists of a set of nodes ( vertices ) and a set of edges that relate the nodes to each other The set of edges describes relationships among the vertices
- 3. Node: Vertex point junction Edge: Give path. TYPES OF GRAPHS: 1)Directed 2)Undirected
- 4. Undirected graphs When the edges in a graph have no direction, the graph is called undirected edges do not have a direction (V1, V2) and (V2, V1) are the same edge
- 5. When the edges in a graph have a direction, the graph is called directed (or digraph ) Directed graphs E(Graph2) = {(1,3) (3,1) (5,9) (9,11) (5,7) edges have a direction <V1, V2> and <V2, V1> are different edges
- 6. Graph implementation Array-based implementation A 1D array is used to represent the vertices A 2D array (adjacency matrix) is used to represent the edges
- 8. Linked-list implementation A 1D array is used to represent the vertices A list is used for each vertex v which contains the vertices which are adjacent from v (adjacency list)
- 10. Traversing a graph Where to start? Will all vertices be visited? How to prevent multiple visits?
- 11. Graph searching Depth-First-Search (DFS) or Breadth-First-Search (BFS)
- 12. depth first traversal depthFirstTraversal (v) visit v mark v as visited for each neighbor (u) of v if not yet visited depthFirstTraversal (u)
- 13. Set found to false stack.Push(startVertex) DO stack.Pop(vertex) IF vertex == endVertex Set found to true ELSE Push all adjacent vertices onto stack WHILE !stack.IsEmpty() AND !found IF(!found) Write "Path does not exist" Depth-First-Search (DFS)
- 14. Depth-First-Search (DFS) What is the idea behind DFS? Travel as far as you can down a path DFS can be implemented efficiently using a stack
- 18. Breadth-First-Searching (BFS) What is the idea behind BFS? Look at all possible paths at the same depth before you go at a deeper level
- 19. breadth first traversal Breadth First Traversal (v) put v in Q while Q not empty remove w from Q visit w mark w as visited for each neighbor (u) of w if not yet visited put u in Q
- 20. BFS can be implemented efficiently using a queue Set found to false queue.Enqueue(startVertex) DO queue.Dequeue(vertex) IF vertex == endVertex Set found to true ELSE Enqueue all adjacent vertices onto queue WHILE !queue.IsEmpty() AND !found Breadth-First-Searching (BFS) IF(!found) Write "Path does not exist"
- 22. next:
- 24. EXAMPLES OF GRAPHS IN OUR DAILY LIFE FACEBOOK ,TWITTER,OTHER SOCAIL NETWORKS
- 25. some problems that can be represented by a graph computer networks airline flights road map course prerequisite structure tasks for completing a job flow of control through a program many more
- 26. Types of Graphs SIMPLE GRAPH At most one edge between any pair of nodes.
- 27. Notation of graphs A graph G is defined as follows: G=(V,E) V(G): a finite, nonempty set of vertices E(G): a set of edges (pairs of vertices)
- 28. Multigraph Multiple edges between nodes are allowed
- 29. Pseudographs Self loops are permitted.
- 30. Trees are special cases of graphs!! Trees vs graphs