Vertices and edges model networks; stored as adjacency lists or matrices.
A graph has vertices and edges (directed or undirected, weighted or not). Representations: adjacency list (O(V+E) space) and adjacency matrix (O(V²)). Graphs model networks, maps, dependencies and social connections. Properties: connectivity, cycles, degree.
Cities as vertices and roads as weighted edges form a road network.
Graphs model relationships between things, and they are used for maps, networks, dependencies and social systems.
Vertices and edges model networks; stored as adjacency lists or matrices.
Graphs model relationships between things, and they are used for maps, networks, dependencies and social systems.
As adjacency lists, which are efficient for sparse graphs, or adjacency matrices, which give fast edge checks for dense graphs.
In a directed graph each edge has a direction, such as one-way roads, while undirected edges go both ways, such as two-way links.
Typical applications include modelling a road network for route planning, representing the dependencies between software modules in a build and describing a power grid as nodes and lines for analysis.
Study "Heaps and priority queues" first (topic 24 of 104 in Software & Computing). It covers the groundwork this topic builds on.
Directed acyclic graphs. Sparse vs dense. Bipartite graphs.
Cities as vertices and roads as weighted edges form a road network.
The next topic is "BFS and DFS", which builds directly on this one.
It is classed as Beginner in Software & Computing (topic 25 of 104). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.
Want to practise? Open the interactive course for quick checks, quizzes, simulations and progress tracking.