Graph Theory Terminology: Vertices, Edges, Endpoints

In summary, the picture in the conversation shows numerical values as vertices and the lines connecting them as edges. The endpoints of an edge are the two nodes at each end, but since this is not a directed graph, there are no incoming or outgoing edges.
  • #1
Gear2d
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I was wondering if I could get some help with the terminology when it comes to graph theory. In this picture : http://en.wikipedia.org/wiki/Image:6n-graf.svg the numerical values are vertices (or nodes as some call it), so what are the edges then (are they the lines that connect the nodes)? What would be considered a end vertices (endpoints), outgoing edges, and incoming edges?
 
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  • #2
Yes, the lines connecting the numbers are the edges. The "end vertices" or "endpoints" of an edge are the two numbers (nodes) at each end of an edge. Since this is not a directed graph (we are not given a direction to each edge- that is "from" one node "to" the other) there are no "incoming" or "outgoing" edges.
 

FAQ: Graph Theory Terminology: Vertices, Edges, Endpoints

What is a vertex in graph theory?

A vertex, also known as a node, is a fundamental element in a graph that represents a point or object. In other words, it is a location or position in the graph where edges can connect.

What is an edge in graph theory?

An edge is a connection or link between two vertices in a graph. It can be represented by a line or arc and is used to show a relationship or interaction between the two vertices it connects.

Can a vertex have multiple edges?

Yes, a vertex can have multiple edges connecting it to other vertices in a graph. This can represent multiple relationships or interactions with other objects or points in the graph.

What are endpoints in graph theory?

Endpoints are the vertices at the beginning and end of an edge. They are the points where the edge connects to the vertices and are important in determining the direction of the edge.

How are vertices and edges related in a graph?

Vertices and edges are the two main components of a graph and are closely related. Vertices represent the objects or points in the graph, while edges represent the connections or relationships between the vertices. Without vertices, there can be no edges, and without edges, there can be no connections between vertices in a graph.

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