Edge vs. Vertice — What's the Difference?

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.