What is graphs?
A graph is a way to show how things are connected. It’s made up of points called “nodes” (or vertices) and lines called “edges” that link the nodes together. Think of a social network: each person is a node and each friendship is an edge.
Let's break it down
- Nodes: the individual items you want to represent (people, cities, computers, etc.).
- Edges: the relationships or paths between nodes (friendships, roads, data links).
- Directed vs. undirected: In a directed graph, edges have a direction (like a one‑way street); in an undirected graph, they don’t (like a two‑way road).
- Weighted vs. unweighted: A weighted graph gives each edge a number (like distance or cost); an unweighted graph treats all edges the same.
Why does it matter?
Graphs let us model real‑world problems where connections matter. By turning a problem into a graph, we can use math and algorithms to find shortest routes, detect clusters, or discover important nodes. This makes complex systems easier to understand and solve.
Where is it used?
- Social media platforms to suggest friends or content.
- Navigation apps to find the quickest driving route.
- Internet routing to move data between computers.
- Recommendation engines (movies, products) to link similar items.
- Biology for mapping protein interactions or disease spread.
Good things about it
- Very flexible: can represent almost any network of relationships.
- Powerful algorithms exist (like Dijkstra’s, BFS, DFS) that solve many problems efficiently.
- Helps visualize data, making patterns and outliers easier to spot.
- Works well with large data sets when optimized.
Not-so-good things
- Large graphs can consume a lot of memory and processing power.
- Some problems (like finding the optimal traveling salesman route) are computationally hard and may not have fast solutions.
- Building an accurate graph requires good quality data; missing or wrong connections can lead to bad results.
- Visualizing very big graphs can become cluttered and hard to read.