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An adjacency list representation for a graph associates each vertex in the graph with the collection of its neighbouring vertices or edges. There are many variations of this basic idea, differing in the details of how they implement the association between vertices and collections, in how they implement the collections, in whether they include both vertices and edges or only vertices as first ...
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.
Cantera is an open-source chemical kinetics software used for solving chemically reacting laminar flows. It has been used as a third-party library in external reacting flow simulation codes, such as FUEGO and CADS, using Fortran, C++, etc. to evaluate properties and chemical source terms that appear in the application's governing equations.
List of software for Monte Carlo molecular modeling; Comparison of software for molecular mechanics modeling; Molecular design software; Molecule editor; Molecular modeling on GPUs; List of software for nanostructures modeling; Semi-empirical quantum chemistry method; Computational chemical methods in solid-state physics, with periodic boundary ...
A decision version of the problem (testing whether some vertex u occurs before some vertex v in this order) is P-complete, [12] meaning that it is "a nightmare for parallel processing". [13]: 189 A depth-first search ordering (not necessarily the lexicographic one), can be computed by a randomized parallel algorithm in the complexity class RNC ...
It also maintains a value v.lowlink that represents the smallest index of any node on the stack known to be reachable from v through v's DFS subtree, including v itself. Therefore v must be left on the stack if v.lowlink < v.index, whereas v must be removed as the root of a strongly connected component if v.lowlink == v.index.
It is also possible to store edge weights directly in the elements of an adjacency matrix. [12] Besides the space tradeoff, the different data structures also facilitate different operations. Finding all vertices adjacent to a given vertex in an adjacency list is as simple as reading the list, and takes time proportional to the number of neighbors.
A simple decision tree to detect the presence of a 3-clique in a 4-vertex graph. It uses up to 6 questions of the form "Does the red edge exist?", matching the optimal bound n(n − 1)/2. The (deterministic) decision tree complexity of determining a graph property is the number of questions of the form "Is there an edge between vertex u and ...