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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.
An alternative algorithm for topological sorting is based on depth-first search.The algorithm loops through each node of the graph, in an arbitrary order, initiating a depth-first search that terminates when it hits any node that has already been visited since the beginning of the topological sort or the node has no outgoing edges (i.e., a leaf node):
In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. In the special case of a finite simple graph, the adjacency matrix is a (0,1)-matrix with zeros on its diagonal.
As usual with depth-first search, the search visits every node of the graph exactly once, refusing to revisit any node that has already been visited. Thus, the collection of search trees is a spanning forest of the graph. The strongly connected components will be recovered as certain subtrees of this forest.
The name transpose is because the adjacency matrix of the transpose directed graph is the transpose of the adjacency matrix ... which applies depth-first search twice
Adjacency matrix [3] A two-dimensional matrix, in which the rows represent source vertices and columns represent destination vertices. Data on edges and vertices must be stored externally. Only the cost for one edge can be stored between each pair of vertices. Incidence matrix [4]
Adjacency list; Adjacency matrix. Adjacency algebra – the algebra of polynomials in the adjacency matrix; Canadian traveller problem; Cliques and independent sets. Clique problem; Connected component; Cycle space; de Bruijn sequences; Degree diameter problem; Entanglement (graph measure) Erdős–Gyárfás conjecture; Eternal dominating set ...
The depth of a vertex is the length of the path to its root (root path). The depth of a tree is the maximum depth of any vertex. Depth is commonly needed in the manipulation of the various self-balancing trees, AVL trees in particular. The root has depth zero, leaves have height zero, and a tree with only a single vertex (hence both a root and ...