# Edge vs. Vertice — What's the Difference?

By Tayyaba Rehman & Maham Liaqat — Updated on May 21, 2024
Edge refers to the line segment connecting two vertices in a graph or geometric shape, while a vertice (or vertex) is a point where two or more edges meet.

## Key Differences

Edge refers to the straight or curved line segment that connects two vertices in a graph or geometric figure. It is a fundamental component in graph theory, forming the connections between nodes or points. An edge represents a relationship or link between two points. Vertice, more commonly known as vertex (plural: vertices), is the point where two or more edges meet. In geometry, a vertex is the corner point of polygons and polyhedra, such as the tip of a pyramid or the corners of a cube. In graph theory, vertices are the fundamental units connected by edges.
Edge is essential in defining the shape and structure of geometric figures and graphs. It dictates the connections and pathways between points. For instance, in a triangle, the edges are the sides that connect the three vertices. Vertice, on the other hand, marks the position of junctions or intersections in shapes and graphs. Each vertex represents a key point of connection, such as the corner of a polygon or the node in a network.
Edges and vertices together define the topology of a graph or geometric shape. While edges describe the relationships and connections, vertices denote the critical points of these connections.
In computer graphics and computational geometry, edges and vertices are used to model and render 3D shapes. Edges determine the contours and outlines, whereas vertices establish the key points that shape the object.

## Comparison Chart

### Definition

Line segment connecting two vertices
Point where two or more edges meet

### Role in Geometry

Forms sides of polygons and polyhedra
Forms corners or intersections of shapes

### Role in Graph Theory

Represents nodes or points in a graph

### Usage Example

Sides of a triangle
Corners of a cube

### Terminology Variations

None
Also known as vertex (plural: vertices)

## Compare with Definitions

#### Edge

The line where two faces of a polyhedron meet.
The cube has 12 edges.

#### Vertice

A node in a graph or network.
Each vertice in the diagram represented a computer.

#### Edge

The outside limit of an object, area, or surface
She perched on the edge of a desk
A willow tree at the water's edge

#### Vertice

A corner point of a polygon or polyhedron.
The vertices of the cube were labeled.

#### Edge

The sharpened side of the blade of a cutting implement or weapon
A knife with a razor-sharp edge

#### Vertice

A key point defining the shape of a geometric figure.

#### Edge

A quality or factor which gives superiority over close rivals
His cars have the edge over his rivals'

#### Vertice

A point where two or more edges meet.
The corner of the triangle is a vertice.

#### Edge

Provide with a border or edge
The pool is edged with paving

#### Vertice

An intersection point in a geometric shape.
The hexagon has six vertices.

#### Edge

Move or cause to move gradually or furtively in a particular direction
Hazel quietly edged him away from the others
She tried to edge away from him

#### Vertice

(non-standard) vertex

#### Edge

Give an intense or sharp quality to
The bitterness that edged her voice

#### Edge

Strike (the ball) with the edge of the bat; strike a ball delivered by (the bowler) with the edge of the bat
Haynes edged to slip
He edged a ball into his pad

#### Edge

Ski with one's weight on the edges of one's skis
You will be edging early, controlling a parallel turn

#### Edge

A thin, sharpened side, as of the blade of a cutting instrument.

#### Edge

The degree of sharpness of a cutting blade.

#### Edge

A penetrating, incisive quality
"His simplicity sets off the satire, and gives it a finer edge" (William Hazlitt).

#### Edge

A slight but noticeable sharpness, harshness, or discomforting quality
His voice had an edge to it.

#### Edge

Keenness, as of desire or enjoyment; zest
The brisk walk gave an edge to my appetite.

#### Edge

The line or area farthest away from the middle
Lifted the carpet's edge.

#### Edge

The line of intersection of two surfaces
The edge of a brick.

#### Edge

A rim or brink
The edge of a cliff.

#### Edge

The point at which something is likely to begin
On the edge of war.

#### Edge

A margin of superiority; an advantage
A slight edge over the opposition.

#### Edge

To give an edge to (a blade); sharpen.

#### Edge

To tilt (a ski or both skis) in such a way that an edge or both edges bite into the snow.

#### Edge

To put a border or edge on
Edged the quilt with embroidery.

#### Edge

To act as or be an edge of
Bushes that edged the garden path.

#### Edge

The dog edged the ball with its nose.

#### Edge

To trim or shape the edge of
Edge a lawn.

#### Edge

To surpass or beat by a small margin. Often used with out
The runner edged her opponent out at the last moment.

#### Edge

The child edged toward the door.

#### Edge

The boundary line of a surface.

#### Edge

(geometry) A one-dimensional face of a polytope. In particular, the joining line between two vertices of a polygon; the place where two faces of a polyhedron meet.

#### Edge

I have the edge on him.

#### Edge

The thin cutting side of the blade of an instrument, such as an ax, knife, sword, or scythe; that which cuts as an edge does, or wounds deeply, etc.

#### Edge

A sharp terminating border; a margin; a brink; an extreme verge.
The cup is right on the edge of the table.
He is standing on the edge of a precipice.

#### Edge

Sharpness; readiness or fitness to cut; keenness; intenseness of desire.

#### Edge

The border or part adjacent to the line of division; the beginning or early part (of a period of time)
In the edge of evening

#### Edge

(cricket) A shot where the ball comes off the edge of the bat, often unintentionally.

#### Edge

(graph theory) A connected pair of vertices in a graph.

#### Edge

A level of sexual arousal that is maintained just short of reaching the point of inevitability, or climax.

#### Edge

The point of data production in an organization (the focus of edge computing), as opposed to the cloud.

#### Edge

(transitive) To move an object slowly and carefully in a particular direction.
He edged the book across the table.
The muggers edged her into an alley and demanded money.

#### Edge

(intransitive) To move slowly and carefully in a particular direction.
He edged away from her.

#### Edge

(usually in the form 'just edge') To win by a small margin.

#### Edge

To hit the ball with an edge of the bat, causing a fine deflection.

#### Edge

(transitive) To trim the margin of a lawn where the grass meets the sidewalk, usually with an electric or gas-powered lawn edger.

#### Edge

(transitive) To furnish with an edge; to construct an edging.

#### Edge

To furnish with an edge, as a tool or weapon; to sharpen.

#### Edge

(figurative) To make sharp or keen; to incite; to exasperate; to goad; to urge or egg on.

#### Edge

To delay one's orgasm so as to remain almost at the point of orgasm.

#### Edge

The thin cutting side of the blade of an instrument; as, the edge of an ax, knife, sword, or scythe.
He which hath the sharp sword with two edges.
Slander,Whose edge is sharper than the sword.

#### Edge

Any sharp terminating border; a margin; a brink; extreme verge; as, the edge of a table, a precipice.
Upon the edge of yonder coppice.
In worst extremes, and on the perilous edgeOf battle.
Pursue even to the very edge of destruction.

#### Edge

Sharpness; readiness or fitness to cut; keenness; intenseness of desire.
The full edge of our indignation.
Death and persecution lose all the ill that they can have, if we do not set an edge upon them by our fears and by our vices.

#### Edge

The border or part adjacent to the line of division; the beginning or early part; as, in the edge of evening.

#### Edge

To furnish with an edge as a tool or weapon; to sharpen.
To edge her champion's sword.

#### Edge

To shape or dress the edge of, as with a tool.

#### Edge

To furnish with a fringe or border; as, to edge a dress; to edge a garden with box.
Hills whose tops were edged with groves.

#### Edge

To make sharp or keen, figuratively; to incite; to exasperate; to goad; to urge or egg on.
By such reasonings, the simple were blinded, and the malicious edged.

#### Edge

To move by little and little or cautiously, as by pressing forward edgewise; as, edging their chairs forwards.

#### Edge

To move sideways; to move gradually; as, edge along this way.

#### Edge

To sail close to the wind.
I must edge up on a point of wind.

#### Edge

The boundary of a surface

#### Edge

A sharp side formed by the intersection of two surfaces of an object;
He rounded the edges of the box

#### Edge

A line determining the limits of an area

#### Edge

The attribute of urgency;
His voice had an edge to it

#### Edge

He had an edge on the competition

#### Edge

A strip near the boundary of an object;
He jotted a note on the margin of the page

#### Edge

Advance slowly, as if by inches;
He edged towards the car

#### Edge

Provide with a border or edge;
Edge the tablecloth with embroidery

#### Edge

Lie adjacent to another or share a boundary;
England marches with Scotland

#### Edge

Provide with an edge;

#### Edge

A line segment between two points.
The edge of the square was 5 cm long.

#### Edge

A boundary line of a polygon.
The triangle has three edges.

#### Edge

A connection between two nodes in a graph.
Each edge in the network graph represented a friendship.

#### Edge

A part of a geometric figure defining its shape.
The edges of the pentagon were equal.

## Common Curiosities

#### What shapes have vertices?

Polygons, polyhedra, and graphs all have vertices.

#### Can a vertex connect more than two edges?

Yes, a vertex can be the meeting point for multiple edges.

#### What is a vertice?

A vertice, or vertex, is a point where two or more edges meet.

#### How do edges and vertices differ in graph theory?

Edges represent connections or links, while vertices represent nodes or points.

#### Do edges have lengths?

Yes, in geometry, edges have measurable lengths.

#### Is a vertice the same as a vertex?

Yes, vertice is an alternate term for vertex; the plural is vertices.

#### How are edges important in graph theory?

Edges are crucial for defining the relationships between nodes.

#### What is an edge in geometry?

An edge is a line segment that connects two vertices in a geometric shape.

#### Can edges be curved?

Yes, edges can be straight or curved, depending on the shape.

#### What is a common example of an edge in everyday life?

The edge of a table or a piece of paper is a common example.

#### How many vertices does a triangle have?

A triangle has three vertices.

#### What is the role of vertices in polygons?

Vertices are the corner points that define the shape of polygons.

#### How are edges used in 3D modeling?

Edges define the contours and connections in 3D models.

#### What determines the number of edges in a polyhedron?

The number of faces and vertices typically determines the number of edges.

#### Do vertices have coordinates?

Yes, vertices are often defined by their coordinates in space.

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