Graph Data Structure and Algorithms (Example)

By : Sarah Chen Sarah Chen
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⚡ Smart Summary

Graph Data Structure is a non-linear collection of vertices and edges where each edge links a pair of vertices. Graphs model real-world networks such as maps, social connections, and web pages, and support many powerful algorithms.

  • 📐 Structure: A graph G = (V, E) pairs a set of vertices (nodes) with a set of edges (links) between them.
  • 🔤 Terminology: Key terms include vertex, edge, degree, indegree, outdegree, self-loop, and adjacency.
  • 🗂️ Representation: Graphs are stored using an adjacency matrix or an adjacency list, each with different space trade-offs.
  • 🧭 Types: Directed, undirected, weighted, cyclic, acyclic, complete, bipartite, and more classify graphs by structure.
  • 🌐 Applications: Google Maps routing, social networks, web ranking, and resource dependency all rely on graphs.
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Graph Data Structure and Algorithms

What is a Graph in Data Structure?

A graph is a non-linear data structure that consists of vertices and edges, where vertices contain the information or data, and the edges work as a link between a pair of vertices.

It is used to solve real-world problems like finding the best route to the destination location and the route for telecommunications and social networks. Users are considered a node in the Graph, and the wires are the edges connecting the users.

If edges are represented as E and vertices are represented as V, then the graph G can be written as the set of vertices and edges, such as G (V, E).

Example of Graph in Data Structure

Here is a simple example of a graph data structure:

Example of Graph in Data Structure

It is a simple undirected graph (one kind of Graph). Here the set of vertices is: {A, B, C, D, E, F}. Two vertices create an edge. For example, A and B are linked with an edge. However, A and F are not linked with any edges.

Graph Terminologies in Data Structure

The following are some important terms used in the graph data structure:

TermDescription
VertexEach data element is called a vertex or a node. In the above image, A, B, C, D & E are the vertices.
Edge (Arc)Connecting links between two nodes or vertices are called an edge (Arc). It has two ends and is represented as (startingVertex, endingVertex).
Undirected EdgeIt is a bidirectional edge.
Directed EdgeIt is a unidirectional edge.
Weighted EdgeAn edge with a value on it.
DegreeIn a Graph, the number of edges connected to a vertex is called a degree.
IndegreeThe total number of incoming edges connected to a vertex.
OutdegreeThe total number of outgoing edges connected to a vertex.
Self-loopAn edge is called a self-loop if its two endpoints coincide.
AdjacencyVertices are said to be adjacent if an edge is connected between them.

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Types of Graphs in Data Structure

Here is the list of the most common types of graphs in the data structure:

  • Directed Graph
  • Undirected Graph
  • Weighted Graph
  • Bi-Directional Graph
  • Infinite Graph
  • Null Graph
  • Trivial Graph
  • Multi Graph
  • Complete Graph
  • Connected Graph
  • Cyclic Graph
  • Directed Acyclic Graph (DAG)
  • Cycle Graph
  • Bipartite Graph
  • Euler Graph
  • Hamilton Graph

How to Represent a Graph in Data Structure?

A graph is commonly stored in memory using one of two representations. The choice affects how much memory the graph uses and how fast common operations run.

  • Adjacency Matrix: A two-dimensional V × V array where cell [i][j] is 1 (or the edge weight) if an edge exists between vertex i and vertex j, and 0 otherwise. It allows O(1) edge lookup but uses O(V²) space, making it best for dense graphs.
  • Adjacency List: An array of lists where each vertex stores a list of its neighbouring vertices. It uses O(V + E) space and is efficient for sparse graphs, which is why most real-world graphs use it.

You can read more about these in the adjacency list and matrix representation of a graph tutorial.

Applications of Graph Data Structure

A graph has many use cases. There are a lot of algorithms that use Graphs. Here are some of the applications of the Graph:

  • Google Maps uses graphs to find the intersection of two roads and calculate the distance between two locations. For example, Dijkstra, for finding the shortest distance between the source and destination location.
  • Facebook uses Graphs to find the mutual friends of the users. Its algorithm considers each user as a node of a graph.
  • For resource allocation, a DAG (Directed Acyclic Graph) is used. It checks the dependency of the resources.
  • The Google Search Engine uses graphs to create the ranking for websites.
  • A mapping device uses the graph data structure.
  • A Router and its protocol use the Graph to learn the path to the destination.

FAQs

Graph Neural Networks learn from graph-structured data for fraud detection, recommendations, and drug discovery. Knowledge graphs support AI question-answering, and deep learning frameworks model every computation as a graph of operations.

Yes. AI assistants like GitHub Copilot can generate BFS, DFS, Dijkstra, and topological sort implementations from a plain description. You should still test edge cases such as disconnected nodes, cycles, and empty graphs before using the code.

A tree is a special type of graph that is connected and has no cycles, with exactly one path between any two nodes. A graph is more general: it can contain cycles, disconnected parts, and directed or weighted edges.

The two main traversal methods are Breadth-First Search (BFS), which explores level by level using a queue, and Depth-First Search (DFS), which explores as deep as possible using a stack or recursion before backtracking.

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