Graphs

When is an edge incident?

When it is on the two vertices it connects

When are two vertices adjacent (or neighbors)?

When they are connected by an edge

cycle

path with the first and last node equal

Directed graph

A graph in which the edges have direction

DAG

directed acyclic graph

topological sort

listing of nodes such that if (a,b) is an edge, a appears before b in the list

Do the nodes in graphs have to be hierarchical?

No

complete graph

a graph in which all nodes are adjacent

precedence graph

a graph in which an edge from x to y indicates x should come before y (is a DAG)

weighted graph

a graph in which the edges have a weight

graph

a set of nodes connected by edges

simple path

all nodes are distinct

depth-first search

builds a spanning tree of all of the reachable nodes from the staring vertex v, using marking of the visited nodes

acyclic graph

graph without cycles

adjacency matrix

matrix with entries that indicate if an edge between two vertices is present (in a weighted graph entries are the weights)

topological sort algorithm

modification of DFS, traverse tree using DFS starting from all nodes that have no predecessor, add a node to the list when ready to backtrack

path

sequence of nodes that are connected to each other

path length

the number of edges in the path, or the sum of weights

in-degree of a vertex

the number of edges pointing into the vertex

out-degree of a vertex

the number of edges pointing out of the vertex

breadth-first search

visits the nodes of a graph in breadth-first order, results in a spanning tree