Graphs

Internal

• Data Structures

Overview

Graphs are fundamental structures in computer science. They apply directly to a large number of problems that involve physical networks - such as the phone network or the internet, or logical networks about parallel relationships between objects in general - the order in which to execute interdependent tasks, or the analysis of social networks.

Graphs are backed by mathematical formalism. The Graph Concepts page provides a number of terms, concepts and some mathematical tools that are useful when dealing with graphs. Graph Representation in Memory describes ways to represent graph nodes and edges in such a way that they can be manipulated by algorithms. The most common arrangements - adjacency lists and adjacency matrices - are discussed.

The most obvious problem that arises when dealing with graphs is to walk them: search the graph or find paths through graphs, or more generically, explore a graph and infer knowledge about it. The classical algorithms for graph exploration are breadth-first search (BFS) and depth-first search (DFS). Both these algorithms are very efficient, they are capable of exploring the graph in linear time of the number of vertices and edges O(n + m). They are described and discussed in the Graph Search page.

Building upon the basic graph search algorithms, we discuss several useful graph problems: computing the shortest path between two vertices using breadth-first search, clustering heuristics by finding connected components in an undirected graph with breadth-first search, finding strongly connected components in a directed graph with depth-first search and the topological sort of a directed acyclic graph with depth-first search.

Subjects

• Graph Concepts
• Graph Representation in Memory
• Graph Search
• Shortest Path in a Graph with breadth-first search
• Find Connected Components in an Undirected Graph with breadth-first search
• Find Strongly Connected Components in an Directed Graph with depth-first search
• Topological Sort of a Directed Acyclic Graph with depth-first search