Edge vs. Vertex — What's the Difference?
By Fiza Rafique & Urooj Arif — Updated on May 9, 2024
An edge in a graph theory represents a connection between two vertices, while a vertex is a point where edges meet or terminate.
Difference Between Edge and Vertex
Table of Contents
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Key Differences
In graph theory, an edge is a line that connects two vertices, suggesting a relationship or pathway between them. A vertex (or node), however, is one of the fundamental units that make up the structure of a graph, representing endpoints or intersections of edges.
Edges are crucial for defining the connectivity between vertices, enabling the graph to illustrate networks such as social connections, computer networks, or maps. In contrast, vertices serve as critical points of data, decisions, or locations within the graph.
The role of an edge is to express the type and strength of the relationship between vertices. For example, in weighted graphs, edges have values that represent the cost or distance between vertices. Meanwhile, vertices might be used to represent entities such as cities in a map, where each city is a vertex.
Graphically, an edge is depicted as a line or arc that may be directed (indicating one-way interaction) or undirected. Vertices are usually shown as dots or circles, often labeled with letters or numbers to provide information or to identify them.
In algorithms, the efficiency often depends on the number of vertices and edges in a graph. Operations such as traversing or searching a graph involve moving through edges to reach various vertices, highlighting their interdependent nature.
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Comparison Chart
Definition
Connects two vertices in a graph
A point in a graph where edges meet
Role in Graphs
Indicates relationships and pathways
Acts as a fundamental unit, a data point
Graphical Representation
Depicted as lines or arcs between dots
Represented as dots or circles in a graph
Importance in Algorithms
Used to traverse between points in a graph
Served as critical points for data or decisions
Example in Practical Use
Roads in a transportation network
Cities or intersections in a transportation network
Compare with Definitions
Edge
A line connecting two vertices in a graph.
In a friendship network graph, an edge represents a friendship link between two people.
Vertex
Represents entities or locations in models.
Each vertex in a city traffic map might represent an intersection or endpoint.
Edge
Often carries weight in weighted graphs.
An edge in a network graph might represent the distance or cost between nodes.
Vertex
A point where edges converge in a graph.
In a computer network, each computer is a vertex connected by network links (edges).
Edge
Can be directed or undirected.
A directed edge in a graph indicates a one-way street between two points.
Vertex
Labeled for identification in complex graphs.
Vertices in a molecular structure are labeled with element symbols.
Edge
Represents relationships in abstract models.
An edge in a project dependency graph shows the prerequisite relationships between tasks.
Vertex
Used to represent decision or data points in algorithms.
Each vertex in a decision tree represents a decision or classification point.
Edge
Integral for defining graph structure.
Edges determine the connectivity pattern in a neural network.
Vertex
Can be entry or exit points in pathfinding.
Vertices in a maze are critical points where decisions are made.
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
Vertex
The highest point; the top or apex.
Edge
The sharpened side of the blade of a cutting implement or weapon
A knife with a razor-sharp edge
Vertex
Each angular point of a polygon, polyhedron, or other figure.
Edge
A quality or factor which gives superiority over close rivals
His cars have the edge over his rivals'
Vertex
The highest point; the apex or summit
The vertex of a mountain.
Edge
Provide with a border or edge
The pool is edged with paving
Vertex
The highest point of the skull.
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
Vertex
The top of the head.
Edge
Give an intense or sharp quality to
The bitterness that edged her voice
Vertex
In astrology, the highest point reached in the apparent motion of a celestial body.
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
Vertex
The point at which the sides of an angle intersect.
Edge
Ski with one's weight on the edges of one's skis
You will be edging early, controlling a parallel turn
Vertex
The point on a triangle or pyramid opposite to and farthest away from its base.
Edge
A thin, sharpened side, as of the blade of a cutting instrument.
Vertex
A point on a polyhedron common to three or more sides.
Edge
The degree of sharpness of a cutting blade.
Vertex
A point of maximal curvature on a parabola or hyperbola.
Edge
A penetrating, incisive quality
"His simplicity sets off the satire, and gives it a finer edge" (William Hazlitt).
Vertex
The highest point, top or apex of something.
Edge
A slight but noticeable sharpness, harshness, or discomforting quality
His voice had an edge to it.
Vertex
(anatomy) The highest surface on the skull; the crown of the head.
Edge
Keenness, as of desire or enjoyment; zest
The brisk walk gave an edge to my appetite.
Vertex
(geometry) An angular point of a polygon, polyhedron or higher order polytope.
Edge
The line or area farthest away from the middle
Lifted the carpet's edge.
Vertex
The common point of the two rays that form an angle.
Edge
The line of intersection of two surfaces
The edge of a brick.
Vertex
The point at which an axis meets a curve or surface.
Edge
A rim or brink
The edge of a cliff.
Vertex
(mathematics) A point on the curve with a local minimum or maximum of curvature.
Edge
The point at which something is likely to begin
On the edge of war.
Vertex
(graph theory) One of the elements of a graph joined or not by edges to other vertices.
Edge
A margin of superiority; an advantage
A slight edge over the opposition.
Vertex
(computer graphics) A point in 3D space, usually given in terms of its Cartesian coordinates.
Edge
To give an edge to (a blade); sharpen.
Vertex
(optics) The point where the surface of a lens crosses the optical axis.
Edge
To tilt (a ski or both skis) in such a way that an edge or both edges bite into the snow.
Vertex
(particle physics) An interaction point.
Edge
To put a border or edge on
Edged the quilt with embroidery.
Vertex
(astrology) The point where the prime vertical meets the ecliptic in the western hemisphere of a natal chart.
Edge
To act as or be an edge of
Bushes that edged the garden path.
Vertex
(typography) A sharp downward point opposite a crotch, as in the letters "V" and "W" but not "Y".
Edge
To advance or push slightly or gradually
The dog edged the ball with its nose.
Vertex
A turning point; the principal or highest point; top; summit; crown; apex.
Edge
To trim or shape the edge of
Edge a lawn.
Vertex
The top, or crown, of the head.
Edge
To surpass or beat by a small margin. Often used with out
The runner edged her opponent out at the last moment.
Vertex
The zenith, or the point of the heavens directly overhead.
Edge
To move gradually or hesitantly
The child edged toward the door.
Vertex
The point in any figure opposite to, and farthest from, the base; the terminating point of some particular line or lines in a figure or a curve; the top, or the point opposite the base.
Edge
The boundary line of a surface.
Vertex
The point of intersection of lines or the point opposite the base of a figure
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.
Vertex
The highest point (of something);
At the peak of the pyramid
Edge
An advantage.
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
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
A slight competitive advantage;
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;
Canada adjoins the U.S.
England marches with Scotland
Edge
Provide with an edge;
Edge a blade
Common Curiosities
What is a vertex in graph theory?
A point in a graph where two or more edges meet, acting as a fundamental unit.
Are edges more important than vertices in a graph?
Both are crucial for different reasons; edges define relationships, while vertices serve as points of connection or data.
Can a graph exist without edges?
Yes, such a graph would simply have isolated vertices with no connections.
Why are vertices important in algorithms?
They often represent critical data points or decision nodes in computational processes.
Can a graph exist without vertices?
No, a graph must have at least one vertex; without vertices, there’s nothing to connect.
What is an edge in graph theory?
It’s a line connecting two vertices, representing a relationship or pathway.
How many edges can connect to a single vertex?
It varies; a vertex can have as few edges as none or multiple, depending on the graph structure.
How are edges represented in a directed graph?
As arrows pointing from one vertex to another, indicating the direction of the relationship.
What does a weighted edge represent?
It typically represents a value like cost, distance, or capacity between vertices in a graph.
What’s an example of a real-world application of vertices and edges?
Traffic management systems use vertices to represent intersections and edges to represent roads, helping in route optimization and traffic flow analysis.
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Written by
Fiza RafiqueFiza Rafique is a skilled content writer at AskDifference.com, where she meticulously refines and enhances written pieces. Drawing from her vast editorial expertise, Fiza ensures clarity, accuracy, and precision in every article. Passionate about language, she continually seeks to elevate the quality of content for readers worldwide.
Co-written by
Urooj ArifUrooj is a skilled content writer at Ask Difference, known for her exceptional ability to simplify complex topics into engaging and informative content. With a passion for research and a flair for clear, concise writing, she consistently delivers articles that resonate with our diverse audience.
