Please enable JavaScript.

Coggle requires JavaScript to display documents.

Graphs - Coggle Diagram

- - - - If all vertices of a path are distinct, the path is said to be simple.
      - A direct path is a sequence of vertices in which every consecutive pair of the vertices is connected by an edge directed from the vertex listed first to the vertex listed next
- - - - one row and one column for each of the graph’s vertices
        
        in which the element in the i th row and the j th column is equal to:
        
        1
        
        if there is an edge from the i th vertex to the j th vertex
        
        0
        
        if there is no such edge
    - - one for each vertex
        
        that contain all the vertices adjacent to the list’s vertex
      - If a graph is sparse
        
        adjacency list representation
        
        Uses less space than the corresponding adjacency matrix despite the extra storage consumed by pointers of the linked lists
        
        The situation is exactly opposite for dense graphs
  - - - These numbers are called weights or costs
    - - If a weighted graph is represented by its adjacency matrix, then its element A[i,j] will simply contain the weight of the edge from the ith to the j th vertex if there is such an edge and a special symbol if there is no such edge
- - - - If these pairs of vertices are unordered
        
        a pair of vertices (u, v) is the same as the pair (v, u)
        
        the vertices u and v are adjacent to each other and that they are connected by the undirected edge (u, v)
        
        the vertices u and v are endpoints of the edge (u, v)
        and say that u and v are incident to this edge
        
        A graph G is called undirected if every edge in
        it is undirected.
        
        a pair of vertices (u, v) is not the same as the pair (v, u)
        
        the edge (u, v) is directed from the vertex u
        
        (u) the edge’s tail
        
        (v) the edge’s head.
        
        A graph whose every edge is directed is called directed
        
        Directed graphs are also called digraphs.
      - A graph with every pair of its vertices connected by an edge is called complete.
      - A graph with relatively few possible edges missing is called dense
      - A graph with few edges relative to the number of its vertices is called sparse.