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UML class diagram of a Graph (abstract data type) The basic operations provided by a graph data structure G usually include: [1] adjacent(G, x, y): tests whether there is an edge from the vertex x to the vertex y; neighbors(G, x): lists all vertices y such that there is an edge from the vertex x to the vertex y;
Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores as far as possible along each branch before backtracking.
Given a graph G(V,E) and a subset T⊆V, define cutset(T) as the set of edges that connect T with V\T. The cutset structure is a data structure that, without keeping the entire graph in memory, can quickly find an edge in the cutset, if such an edge exists. [7] Start by giving a number to each vertex.
For a graph with E edges and V vertices, Kruskal's algorithm can be shown to run in time O(E log E) time, with simple data structures. This time bound is often written instead as O ( E log V ) , which is equivalent for graphs with no isolated vertices, because for these graphs V /2 ≤ E < V 2 and the logarithms of V and E are again within a ...
Input: A graph G and a starting vertex root of G. Output: Goal state.The parent links trace the shortest path back to root [9]. 1 procedure BFS(G, root) is 2 let Q be a queue 3 label root as explored 4 Q.enqueue(root) 5 while Q is not empty do 6 v := Q.dequeue() 7 if v is the goal then 8 return v 9 for all edges from v to w in G.adjacentEdges(v) do 10 if w is not labeled as explored then 11 ...
An example of CSR representation of a directed graph. Pennant data structure for k=0 to k=3. An example of bag structure with 23 elements. There are some special data structures that parallel BFS can benefit from, such as CSR (Compressed Sparse Row), bag-structure, bitmap and so on.
This graph becomes disconnected when the right-most node in the gray area on the left is removed This graph becomes disconnected when the dashed edge is removed.. In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more ...
Pages in category "Graph data structures" The following 34 pages are in this category, out of 34 total. This list may not reflect recent changes. ...