Connected graph
A connected graph is a graph in which every pair of vertices is joined by a path.
Classic Computer Science Problems in Swift: Essential techniques for practicing programmers
A connected graph is a graph in which a path exists between every pair of vertices.
- How it is used
- Uses connectivity to frame practical network-design problems requiring every node to remain reachable.
- How deep it goes
- Defines connectivity and relates it to spanning trees, but defers a standalone connectivity algorithm.
- Examples
- Illustrates connectivity through a weighted metropolitan-area network and its minimum spanning tree.
- What you can do after
- Evaluate whether a graph can support a spanning tree covering every vertex.
Advanced Algorithms and Data Structures
A connected graph is a graph in which every pair of vertices is joined by a sequence of edges.
- How it is used
- Defines whether graph vertices can reach one another and supports reasoning about components, representations, and planarity.
- How deep it goes
- Defines connectivity, edge bounds, directed-graph distinctions, and planarity consequences without developing a connectivity-testing algorithm.
- Examples
- Uses connected-versus-disconnected figures, tree structure, adjacency representations, and planarity edge bounds.
- What you can do after
- Evaluate graph structure using reachability, minimum-edge reasoning, representation trade-offs, and a preliminary planarity check.
Read how Advanced Algorithms and Data Structures explains connected graph →
Related concepts
- graphkind of · A graph is a mathematical structure consisting of vertices connected by edges that represent relationships or connections.
- connected componenthas part · A connected component is a maximal subgraph in which every pair of vertices is connected by a path.
- treeincludes · A tree is a connected, acyclic structure of nodes, commonly organized hierarchically through parent-child relationships and optionally around a designated root.
- strongly connected componentcontrasts with · A strongly connected component is a maximal set of vertices in a directed graph where every vertex is reachable from every other vertex.
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