What is edges?
An edge is a connection or link between two points, called vertices (or nodes), in a graph. Think of a graph like a simple map: the places you can go are the vertices, and the roads that let you travel between them are the edges.
Let's break it down
- Vertex (node): A single point or item in the graph.
- Edge: The line that joins two vertices.
- Undirected edge: Shows a two‑way connection (you can go both ways).
- Directed edge (or arc): Shows a one‑way connection, often drawn with an arrow.
- Weighted edge: An edge that carries a number (weight) representing cost, distance, or strength.
Why does it matter?
Edges define how things are related or can move between each other. Without edges, a graph would just be a collection of isolated points with no information about relationships, making it useless for modeling real‑world problems like networks, routes, or dependencies.
Where is it used?
- Social networks: People are vertices; friendships or follows are edges.
- Transportation: Cities are vertices; roads, flights, or train tracks are edges.
- Computer networks: Devices are vertices; cables or wireless links are edges.
- Recommendation systems: Items or users are vertices; similarity or interaction is an edge.
- Algorithms: Pathfinding (Dijkstra, A*), network flow, and many others rely on edges.
Good things about it
- Simple to understand and visualize.
- Provides a flexible way to model many different systems.
- Enables powerful algorithms for searching, optimizing, and analyzing connections.
- Can be extended with direction and weight to capture more detail.
Not-so-good things
- Large graphs with many edges can become memory‑intensive and slow to process.
- If edges are not properly defined (e.g., missing direction or weight), the model may give inaccurate results.
- In some cases, overly dense edge connections make the graph hard to read and interpret.