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Several algorithms based on depth-first search compute strongly connected components in linear time.. Kosaraju's algorithm uses two passes of depth-first search. The first, in the original graph, is used to choose the order in which the outer loop of the second depth-first search tests vertices for having been visited already and recursively explores them if not.
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 ...
A graph with three components. In graph theory, a component of an undirected graph is a connected subgraph that is not part of any larger connected subgraph. The components of any graph partition its vertices into disjoint sets, and are the induced subgraphs of those sets. A graph that is itself connected has exactly one component, consisting ...
The problem of graph exploration can be seen as a variant of graph traversal. It is an online problem, meaning that the information about the graph is only revealed during the runtime of the algorithm. A common model is as follows: given a connected graph G = (V, E) with non-negative edge weights. The algorithm starts at some vertex, and knows ...
A connected graph G with the same vertex set as a connected hypergraph H is a host graph for H if every hyperedge of H induces a connected subgraph in G. For a disconnected hypergraph H, G is a host graph if there is a bijection between the connected components of G and of H, such that each connected component G' of G is a host of the ...
In an undirected graph, reachability between all pairs of vertices can be determined by identifying the connected components of the graph. Any pair of vertices in such a graph can reach each other if and only if they belong to the same connected component; therefore, in such a graph, reachability is symmetric ( s {\displaystyle s} reaches t ...
In computing and graph theory, a dynamic connectivity structure is a data structure that dynamically maintains information about the connected components of a graph. The set V of vertices of the graph is fixed, but the set E of edges can change. The three cases, in order of difficulty, are:
InfiniteGraph is a distributed graph database implemented in Java and C++ and is from a class of NOSQL ("Not Only SQL") database technologies that focus on graph data structures. Developers use InfiniteGraph to find useful and often hidden relationships in highly connected, complex big data sets.