Graphs in Data Structure: Types, Storing & Traversal
By Rohit Sharma
Updated on May 12, 2025 | 12 min read | 53.25K+ views
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By Rohit Sharma
Updated on May 12, 2025 | 12 min read | 53.25K+ views
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Did you know that facts presented in words and numbers attain 68% attention from viewers? However, a graph claim can raise attention span by 97%. This is where graphs in data structure become important, as they provide a visually stunning way to represent complex relationships and data interaction
Graph terminology in data structure encompasses nodes (vertices), representing entities, and edges, denoting relationships between nodes. It includes concepts like directed edges (arcs) for one-way connections and weighted edges for representing costs or distances. Understanding these terms is essential for manipulating and analyzing graph data effectively.
Professionals often use different types of graphs, such as weighted, directed, and more, to address practical problems, representing the problem area as a particular network. Understanding these terms is essential for manipulating and analyzing graph data effectively.
In this blog, we will explore the role of graphs in data structures, along with their types, storage, and traversal.
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Graphs in data structures are critical for modeling relationships and connections between entities. As fundamental components of modern computing, they represent data through nodes (vertices) and edges, allowing you to express complex relationships in a structured manner. Graphs in data structures can be categorized based on their characteristics. These categories help optimize their representation, storage, and traversal methods to suit specific applications
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Here are the key elements of a graph:
Visualization of Graphs
Graphs can be analyzed visually through tools such as scatter plots, box plots, and histograms to uncover patterns and relationships within the data:
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Now, let’s look at some of the major types of graphs in data structures.
Graphs, in their various types, are used to model real-world relationships, where nodes represent entities, and edges represent the connections between them. In modern computing, understanding the different types of graphs is crucial for selecting the most efficient approach to data manipulation and analysis.
The choice of graph type, weighted or unweighted, directed or undirected, depends mainly on the problem you're solving and the computational constraints. Graphs are implemented using data structures in different programming languages like Python, Java, C#, and C++.
Graphs whose edges or paths have values. All the values seen associated with the edges are called weights. Edges value can represent weight/cost/length.
Values or weights may also represent:
Use Case:
In a real-world scenario like GPS navigation (e.g., Google Maps), weighted graphs are used to find the shortest driving route between two locations. The weights in this case represent the distance or time taken to travel between different points. In Java or Python, libraries like NetworkX or Java's JGraphT can be used to model and process weighted graphs for such applications.
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An unweighted graph does not assign any weights to its edges. Each edge is considered equal in terms of distance or cost. These graphs are typically used for modeling simple relationships without the need for differentiation between connections.
Use Case:
In social networks (e.g., Facebook), an unweighted graph could represent users as nodes, with edges connecting friends. Each edge would have the same significance, showing only whether a user is connected to another, without considering the strength of the relationship. In Python, libraries like NetworkX allow easy construction and manipulation of unweighted graphs for such applications.
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In an undirected graph, edges do not have a direction. The relationship between two nodes is bidirectional, meaning that if there's a connection from node A to node B, you can traverse from B to A. These graphs often represent mutual relationships, such as friendships in social networks
Use Case:
Consider a simple undirected graph for a friendship network on a platform like LinkedIn. Each node represents a user, and an edge between two nodes indicates a mutual connection (friendship). The graph representation is symmetric; if user A is connected to user B, then user B is also connected to user A. In Java, one could use the JGraphT library to model and traverse such undirected graphs for tasks like network analysis.
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A directed graph (also known as a digraph) is a graph with edges that have a direction. Each edge has a starting node and an ending node, meaning the connection from one node to another is one-way. Directed graphs are useful for modeling asymmetric relationships such as flows, dependencies, or causality, where the direction of the relationship matters.
Use Case:
In web crawling (e.g., Google Search Engine), a directed graph can represent web pages as nodes, with directed edges indicating hyperlinks between pages. The direction of the edge signifies the flow from one page to another when a user clicks a link. In Python, frameworks like Scrapy or libraries like NetworkX can create and analyze directed graphs in such use cases.
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Let’s explore the sorting of graphs in data structures for effective data analysis.
Every storage method has its pros and cons, and the right storage method is chosen based on the complexity. The two most commonly used data structures to store graphs are:
The adjacency list is one of the most common ways to represent graphs, especially when the graph is sparse (i.e., not all nodes are connected). Each node is stored as an index in a one-dimensional array, and its edges are stored as a list of adjacent nodes.
This method is memory-efficient, as it only stores the edges that exist. It is often used in web applications, social networks, and other systems where connections are dynamic and frequently updated, like ReactJS applications.
Use Case:
An adjacency list can represent the friendships between users in a React application that manages connections between users. Each user’s ID (node) can be mapped to an array of other user IDs (edges) they are connected to.
This setup is ideal for managing dynamic connections where users may frequently add or remove friends. In React, you could manage the graph using JavaScript objects or arrays, updating the adjacency list as users connect and disconnect.
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Here nodes are represented as the index of a two-dimensional array, followed by edges represented as non-zero values of an adjacent matrix.
Both rows and columns showcase Nodes; the entire matrix is filled with either “0” or “1”, representing true or false. Zero represents that there is no path, and 1 represents a path.
The adjacency matrix is a two-dimensional array that represents a graph, where rows and columns correspond to nodes. Each entry in the matrix indicates whether there is an edge between two nodes. A value of "1" denotes the presence of an edge, while "0" indicates no connection.
This representation benefits dense graphs (where most nodes are connected). It is easy to implement in environments that leverage parallel processing, such as with Docker containers or Kubernetes for scaling. Adjacency matrices are also used in graph neural networks (GNNs) to represent graph structures in machine learning applications like TensorFlow.
Use Case:
In a machine learning model built with TensorFlow, the adjacency matrix can represent the connectivity between nodes in a graph, especially when implementing GNNs. With Kubernetes or Docker, you could scale the matrix operations in a distributed environment, processing graph data across multiple containers for faster computations. This approach is common in applications like social network analysis, where nodes represent users and edges represent interactions or relationships between them.
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I found that graphs in ds can come in different presentations of adjacency matrices, adjacency lists, and edge lists. There is uniqueness in each of the representations as they offer benefits and drawbacks in terms of performance, memory usage and manipulation. Understanding the form of these representations enables us developers to freely select the best one fitting our needs the most.
Let’s understand what graph traversal is in data structures.
Graph traversal is a method used to search nodes in a graph. The traversal of graph in data structure is used to decide the order used for node arrangement. It also searches for edges without making a loop, which means all the nodes and edges can be searched without creating a loop.
There are two graph traversal structures.
The DFS search begins starting from the first node and goes deeper and deeper, exploring down until the targeted node is found. If the targeted key is not found, the search path is changed to the path that was stopped exploring during the initial search, and the same procedure is repeated for that branch.
The spanning tree is produced from the result of this search. This tree method is without the loops. The total number of nodes in the stack data structure is used to implement DFS traversal.
Steps followed to implement DFS search:
Applications of DFS:
1. Solving Puzzles with Only One Solution:
DFS is often used in solving problems like mazes, Sudoku, and other puzzles where only one valid solution exists. By exploring all possible paths recursively, DFS ensures that all potential solutions are tested until the correct one is found.
For example, when solving a Sudoku puzzle using DFS in Python, you can implement backtracking techniques to explore possible number placements recursively.
2. To Test if a Graph is Bipartite:
A graph is bipartite if its vertices can be divided into two disjoint sets such that no two vertices within the same set are adjacent. DFS can be applied to check bipartiteness by attempting to color the graph with two colors.
As you traverse using DFS, you alternate the color of adjacent nodes. However, if you find two adjacent nodes of the same color, the graph is not bipartite. This approach can be implemented in AWS Lambda to scale efficiently for large graphs in cloud-based environments.
3. Topological Sorting for Scheduling Jobs:
DFS is a crucial algorithm in topological sorting, used to order tasks or jobs based on their dependencies. For example, in job scheduling systems like Azure Databricks, tasks must be executed in a specific order based on their dependencies.
The nodes are processed so that all prerequisites (edges) are handled before a task is executed. This makes DFS an essential part of dependency management in cloud computing architectures.
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Breadth-First Search navigates a graph in a breadth motion and utilises based on the Queue to jump from one node to another, after encountering an end in the path.
Steps followed to implement BFS search,
Applications of BFS are:
Real-world Applications of Graph in the Data Structure
Graphs are used in many day-to-day applications like network representation (roads, optical fibre mapping, designing circuit board, etc.). Ex: In the Facebook data network, nodes represent the user, his/her photo or comment, and edges represent photos, comments on the photo.
The Graph in data structure has extensive applications. Some of the notable ones are:
On the Yelp platform, the nodes represent the business, containing id, name, is_closed, and many other graph properties.
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Let’s explore the basic operations of graphs in detail.
Graphs in data structures and algorithms (DSA) serve as fundamental tools for representing complex relationships between entities. These operations allow for efficient management and manipulation of nodes and edges.
Here's a technical breakdown of some of the core functionalities:
Example Scenario:
Consider a graph in a social media platform where each node represents a user, and edges represent friendships. Using graph traversal methods, we can analyze the entire network of users to find specific communities or identify the shortest path between two users. Identifying recurring patterns in user interactions can be used to enhance personalized content delivery or optimize the friend suggestion algorithm.
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Let’s explore some of the common uses of graphs.
I’ve seen in many domains that graph type in DSA is adaptable in applications like social networks, transportation systems, recommendation engines, and bioinformatics. The ability to model relations between entities renders them invaluable for studying complex systems and tackling practical issues.
Graphs in data structures are integral to various applications, providing efficient solutions in diverse fields. They model complex relationships, optimize logistics, enhance social media recommendations, and enable fraud detection. In bioinformatics and e-commerce, graphs uncover insights beyond traditional data structures. Graph databases further enable powerful querying, offering deeper analysis of interconnected datasets.
Now, let’s see when you can use graphs for several enterprise-related data analysis tasks.
Graphs are essential in various advanced algorithms that solve real-world problems efficiently. Dijkstra's Algorithm finds the shortest path between two nodes in weighted graphs. In contrast, Prim's Algorithm helps compute the minimum spanning tree by connecting all nodes with the least weight.
Additionally, graph databases like Neo4j and Amazon Neptune are used for storing and querying complex data, offering advantages over traditional databases for graph-based data analysis.
Dijkstra's Algorithm:
Use case:
GPS navigation for calculating optimal travel routes.
Prim's Algorithm:
Use case:
Network design involves minimizing the cost of connecting multiple points.
Graph Databases:
Use case:
Used by platforms like LinkedIn or Facebook for social graph data to provide real-time connections, recommendations, and relationship queries.
Let’s comprehensively discuss some of the pros and cons of graphs in data analytics.
Graphs in data structures are powerful for modeling complex relationships, offering efficient shortest-path traversal and visual representations that simplify understanding intricate connections. They are well-suited for analyzing continuous data and provide versatile solutions across various domains.
However, handling large-scale graphs introduces computational complexity, long processing times, and challenges maintaining data consistency and concurrency, especially in distributed graph databases.
Here’s a comparative table to address the pros and cons of graphs.
Pros |
Cons |
Modeling Complex Relations: Graphs are a natural way to represent real-world relationships and display connections between entities. | Computational Complexity: Handling large-scale graphs requires significant computational power and memory. |
Efficient Shortest Path Traversal: Well-known algorithms make it efficient to find the shortest paths between nodes. | Long Processing Times: Some operations on complex graphs, especially for large datasets, can consume substantial time. |
Visual Representation: Graphs offer a better understanding of relationships and structures compared to charts, making them easier to visualize. | Data Consistency Challenges: Ensuring consistency and managing concurrency in distributed graph databases can be difficult, especially under high concurrency. |
Analyzing Continuous Data: Graphs are commonly used in continuous data analysis, providing a broad range of applications. | Scalability Issues: As graphs grow larger, maintaining performance and efficiency in operations such as traversal and updates can become increasingly difficult. |
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Graphs in data structures are fundamental for representing complex relationships between entities, offering efficient ways to model interactions in various fields. They are categorized into weighted, unweighted, directed, and undirected graphs, each suited for specific applications.
Storing and traversing graphs can be achieved through adjacency lists and matrices, with algorithms like DFS and BFS enabling graph exploration.
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