Graphs, Trees, Directed Graphs

Weighted, Directed Graph

A graph where each edge has direction and a weight associated with it.

Weighted Graph

A graph with numbers assigned to its edges.

Minimum Spanning Tree

A spanning tree such that the total length of its arcs is as small as possible

Spanning Tree

A subgraph of a graph which includes all the vertices of the graph and is also a tree.

Prerequisite

A task that has to be completely finished prior to the start of the next task.

connected graph

All vertices are connected

Graph

Collection of vertices and edges.

Tree

Connected graph with no loops or circuits. If there are n vertices, there must be n-1 edges.

Minimum Project Time

The least amount of time needed to complete a project including every task.

Minimum Project Time

The length of the critical path.

Critical Path

The sequence of activities in a project that is expected to take the longest to complete. It is the longest path in a directed graph.

Directed Graph

This is a graph where an edge has a direction associated with it, for example, a plane flight that takes off in one location and arrives in another. The return flight would be considered a separate edge.