Connected graph

As explained in 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 Classic Computer Science Problems in Swift: Essential techniques for practicing programmers covers it

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 it assumes

Assumes familiarity with vertices, edges, paths, and graphs while defining connectivity, trees, cycles, and spanning trees.

What you can do after

Evaluate whether a graph can support a spanning tree covering every vertex.

How it connects

Connects connected graphs with vertices, edges, paths, trees, cycles, spanning trees, and minimum spanning trees.

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Also explained in

• 

  liveBookmanning.com
  Advanced Algorithms and Data StructuresA connected graph is a graph in which every pair of vertices is joined by a sequence of edges.

Compare how 2 books explain 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.

This explainer was generated by Manning's knowledge graph from the text of Classic Computer Science Problems in Swift: Essential techniques for practicing programmers. The section links point to the parts of the book it draws on.