• Category
  • >Machine Learning

Dijkstra’s Algorithm: The Shortest Path Algorithm

  • Neelam Tyagi
  • Dec 14, 2020
  • Updated on: Jul 19, 2022
Dijkstra’s Algorithm: The Shortest Path Algorithm title banner

A Dutch computer scientist, Edsger Dijkstra, in 1959, proposed an algorithm that can be applied to a weighted graph. The graph can either be directed or undirected with the condition that the graph needs to embrace a non-negative value on its every edge. He named this algorithm “Dijkstra’s Algorithm” at his name. 

 

Let’s dive right into the blog and we will learn 

 

  1. Introduction to Graphs

  1. What is Dijkstra’s Algorithm?

  2. How to Implement the Dijkstra's Algorithm?

  3. Working Example of Dijkstra's Algorithm

  4. Applications of Dijkstra’s Algorithm

  5. Advantages and Disadvantages of Dijkstra’s Algorithm

 

In the series of blogs, we particularly focus on the detailed study, based on graphs, i.e., Group Theory and knowledge Graph, this blog will serve in building our knowledge base to the next level.


 

Introduction to Graphs

 

In simple words, graphs are data structures that are used to depict connections amidst a couple of elements where these elements are called nodes (or vertex) that generally real-time objects, persons or entities and connections amid nodes are termed as edges. Also, two nodes only get connected if there is an edge between them.

 

"A graph is essentially an interrelationship of nodes/vertices connected by edges."

 

Generally, graphs are suited to real-world applications, such as graphs can be used to illustrate a transportation system/network, where nodes represent facilities that transfer or obtain products and edges show routes or subways that connect nodes. 

 

Graphs can be divided into two parts;

 

  • Undirected Graphs: For every couple of associated nodes, if an individual could move from one node to another in both directions, then the graph is termed as an undirected graph.

 

  • Directed Graphs: For every couple of associated graphs, if an individual could move from one node to another in a specific (single) direction, then the graph is known as the directed graph. In this case, arrows are implemented rather than simple lines in order to represent directed edges.

 

Weighted Graphs

 

The weight graphs are the graphs where edges of the graph have “a weight” or “cost” and also where weight could reflect distance, time, money or anything that displays the “association” amid a couple of nodes it links. These weights are an essential element under Dijkstra's Algorithm. 


 

What is Dijkstra’s Algorithm?

 

What if you are provided with a graph of nodes where every node is linked to several other nodes with varying distance. Now, if you begin from one of the nodes in the graph, what is the shortest path to every other node in the graph? 

 

Well simply explained, an algorithm that is used for finding the shortest distance, or path, from starting node to target node in a weighted graph is known as Dijkstra’s Algorithm.

 

This algorithm makes a tree of the shortest path from the starting node, the source, to all other nodes (points) in the graph.

 

Dijkstra's algorithm makes use of weights of the edges for finding the path that minimizes the total distance (weight) among the source node and all other nodes. This algorithm is also known as the single-source shortest path algorithm.

 

Also Read | Branches of Discrete Mathematics

 

Dijkstra’s algorithm is the iterative algorithmic process to provide us with the shortest path from one specific starting node to all other nodes of a graph. It is different from the minimum spanning tree as the shortest distance among two vertices might not involve all the vertices of the graph.

 

It is important to note that Dijkstra’s algorithm is only applicable when all weights are positive because, during the execution, the weights of the edges are added to find the shortest path.

 

And therefore if any of the weights are introduced to be negative on the edges of the graph, the algorithm would never work properly. However, some algorithms like the Bellman-Ford Algorithm can be used in such cases.

 

It is also a known fact that breadth-first search(BFS) could be used for calculating the shortest path for an unweighted graph, or for a weighted graph that has the same cost at all its edges.

 

But if the weighted graph has unequal costs at all its edges, then BFS infers uniform-cost search. Now what?

 

Instead of extending nodes in order of their depth from the root, uniform-cost search develops the nodes in order of their costs from the root. And a variant of this algorithm is accepted as Dijkstra’s Algorithm.  

 

Generally, Dijkstra’s algorithm works on the principle of relaxation where an approximation of the accurate distance is steadily displaced by more suitable values until the shortest distance is achieved.

 

Also, the estimated distance to every node is always an overvalue of the true distance and is generally substituted by the least of its previous value with the distance of a recently determined path.

 

It uses a priority queue to greedily choose the nearest node that has not been visited yet and executes the relaxation process on all of its edges. (From)

 

Example Involved

 

For example, an individual wants to calculate the shortest distance between the source, A, and the destination, D, while calculating a subpath which is also the shortest path between its source and destination. Let’s see here how Dijkstra’s algorithm works;

 

It works on the fact that any subpath, let say a subpath B to D of the shortest path between vertices A and D is also the shortest path between vertices B and D, i.e., each subpath is the shortest path.

 

Here, Dijkstra’s algorithm uses this property in the reverse direction, that means, while determining distance, we overestimate the distance of each vertex from the starting vertex then inspect each node and its neighbours for detecting the shortest subpath to those neighbours. 

 

This way the algorithm deploys a greedy approach by searching for the next plausible solution and expects that the end result would be the appropriate solution for the entire problem.


 

How to Implement the Dijkstra Algorithm?

 

Before proceeding the step by step process for implementing the algorithm, let us consider some essential characteristics of Dijkstra’s algorithm;

 

  • Basically, the Dijkstra’s algorithm begins from the node to be selected, the source node, and it examines the entire graph to determine the shortest path among that node and all the other nodes in the graph. 

  • The algorithm maintains the track of the currently recognized shortest distance from each node to the source code and updates these values if it identifies another shortest path.

  • Once the algorithm has determined the shortest path amid the source code to another node, the node is marked as “visited” and can be added to the path.

  • This process is being continued till all the nodes in the graph have been added to the path, as this way, a path gets created that connects the source node to all the other nodes following the plausible shortest path to reach each node.

 

Also Read | Types of Statistical Analysis

 

Now explaining the step by step process of algorithm implementation;

 

  1. The very first step is to mark all nodes as unvisited,

  2. Mark the picked starting node with a current distance of 0 and the rest nodes with infinity, 

  3. Now, fix the starting node as the current node,

  4. For the current node, analyse all of its unvisited neighbours and measure their distances by adding the current distance of the current node to the weight of the edge that connects the neighbour node and current node,

  5. Compare the recently measured distance with the current distance assigned to the neighbouring node and make it as the new current distance of the neighbouring node,

  6. After that, consider all of the unvisited neighbours of the current node, mark the current node as visited,

  7. If the destination node has been marked visited then stop, an algorithm has ended, and

  8. Else, choose the unvisited node that is marked with the least distance, fix it as the new current node, and repeat the process again from step 4. 

 

 

Working Example of Dijkstra's Algorithm

 

In the above section, you have gained the step by step process of Dijkstra’s algorithm, now let’s study the algorithm with an explained example.

 

We will calculate the shortest path between node C and the other nodes in the graph.


Displaying the example of the Dijkstra's algorithm

Example of Dijkstra's Algorithm


  1. During the execution of the algorithm, each node will be marked with its minimum distance to node C as we have selected node C. 

 

In this case, the minimum distance is 0 for node C. Also, for the rest of the nodes, as we don’t know this distance, they will be marked as infinity (∞), except node C (currently marked as red dot).


Displaying the Node C as current node

Graphical Representation of Node C as Current Node


  1. Now the neighbours of node C will be checked, i.e, node A, B, and D. We start with B, here we will add the minimum distance of current node (0) with the weight of the edge (7) that linked the node C to node B and get 0+ 7= 7.

 

Now, this value will be compared with the minimum distance of B (infinity), the least value is the one that remains the minimum distance of B, like in this case, 7 is less than infinity, and marks the least value to node B.


Assigning Node B a minimum distance value.

Assign Node B a minimum distance value


  1. Now, the same process is checked with neighbour A. We add 0 with 1 (weight of edge that connects node C to A), and get 1. Again, 1 is compared with the minimum distance of A (infinity), and marks the lowest value.


     

Assigning Node A a minimum distance value.

Assign Node A a minimum distance value


The same is repeated with node D, and marked 2 as lowest value at D.


Assign Node D a minimum distance value

Assign Node D a minimum distance value


Since, all the neighbours of node C have checked, so node C is marked as visited with a green check mark.


 

Displaying the image where node C is marked as visited with green mark.

Marked Node C as visited 


  1. Now, we will select the new current node such that the node must be unvisited with the lowest minimum distance, or the node with the least number and no check mark. Here, node A is the unvisited with minimum distance 1, marked as current node with red dot. 


Graphical Representation of Node A as Current Node

Graphical Representation of Node A as Current Node


We repeat the algorithm, checking the neighbour of the current node while ignoring the visited node, so only node B will be checked.

 

For node B, we add 1 with 3 (weight of the edge connecting node A to B) and obtain 4. This value, 4, will be compared with the minimum distance of B, 7, and mark the lowest value at B as 4. 


Assign Node B a minimum distance value

Assign Node B a minimum distance value


  1. After this, node A marked as visited with a green check mark. The current node is selected as node D, it is unvisited and has a smallest recent distance. We repeat the algorithm and check for node B and E.


 

Graphical Representation of Node D as Current Node

Graphical Representation of Node D as Current Node


For node B, we add 2 to 5, get 7 and compare it with the minimum distance value of B, since 7>4, so leave the smallest distance value at node B as 4. 

 

For node E, we obtain 2+ 7= 9, and compare it with the minimum distance of E which is infinity, and mark the smallest value as node E as 9. The node D is marked as visited with a green check mark.


Marked Node D as visited

Marked Node D as visited


  1. The current node is set as node B, here we need to check only node E as it is unvisited and the node D is visited. We obtain 4+ 1=5, compare it with the minimum distance of the node.

 

As 9 > 5, leave the smallest value at node node E as 5. 

 

We mark D as visited node with a green check mark, and node E is set as the current node.


Depicting Node B as visited with green check mark.

Marked Node B as visited


  1. Since it doesn’t have any unvisited neighbours, so there is not any requirement to check anything. Node E is marked as a visited node with a green mark.


The image is showing the all nodes are marked as visited with green check mark.

Marked Node E as visited


So, we are done as no unvisited node is left. The minimum distance of each node is now representing the minimum distance of that node from node C.

 

Also Read | What is the Confusion Matrix

 

Applications of Dijkstra’s Algorithm

 

Before learning any algorithm, we should know the fundamental purpose of using an algorithm that could help us in real-world applications. Such as, for Dijkstra’s algorithm, we are trying to find the solutions to least path based problems. 

 

For example, if a person wants to travel from city A to city B where both cities are connected with various routes. Which route commonly he/ she should choose?

 

Undoubtedly, we would adopt the route through which we could reach the destination with the least possible time, distance and even cost. 

 

Further, with the discussion, it has various real-world use cases, some of the applications are the following:

 

  • For map applications, it is hugely deployed in measuring the least possible distance and check direction amidst two geographical regions like Google Maps, discovering map locations pointing to the vertices of a graph, calculating traffic and delay-timing, etc.

  • For telephone networks, this is also extensively implemented in the conducting of data in networking and telecommunication domains for decreasing the obstacle taken place for transmission.

  • Wherever addressing the need for shortest path explications either in the domain of robotics, transport, embedded systems, laboratory or production plants, etc, this algorithm is applied.

  • Besides that, other applications are road conditions, road closures and construction, and IP routing to detect Open Shortest Path First.


 

Advantages and Disadvantages of Dijkstra’s Algorithm

 

Discussing some advantages of Dijkstra’s algorithm; 

 

  1. One of the main advantages of it is its little complexity which is almost linear. 

  2. It can be used to calculate the shortest path between a single node to all other nodes and a single source node to a single destination node by stopping the algorithm once the shortest distance is achieved for the destination node.

  3. It only works for directed-, weighted graphs and all edges should have non-negative values.

 

Despite various applications and advantages, Dijkstra’s algorithm has disadvantages also, such as;

 

  1. It does an obscured exploration that consumes a lot of time while processing,

  2. It is unable to handle negative edges,

  3. As it heads to the acyclic graph, so can’t achieve the accurate shortest path, and

  4. Also, there is a need to maintain tracking of vertices, have been visited.

 

Also Read | What is Conditional Probability

 

 

Conclusion

 

Among many, we have discussed the Dijkstra algorithm used for finding the shortest path, however, one of the obstacles while implementing the algorithm on the internet is to provide a full representation of the graph to execute the algorithm as an individual router has a complete outline for all the routers on the internet. We have seen

 

  • Graphs are used to display connections between objects, entities or people, they have the main elements: Nodes and edges.

  • Dijkstra’s algorithm enables determining the shortest path amid one selected node and each other node in a graph.

  • And finally, the steps involved in deploying Dijkstra’s algorithm.

 

Also Read | Statistical Data Analysis

 

I hope you really enjoyed reading this blog and found it useful, for other similar blogs and continuous learning follow us regularly. 

Latest Comments

  • aaronclerk001d6d984c683ee4c38

    Jul 10, 2025

    Holy crap, I went to check my credit score today via Experian and myFICO, finally 811. My wife and I are impressed with the services of PINNACLE CREDIT SPECIALIST. Although I don’t expect this to last too long (I’m buying a house) it is something that I’m proud of. I don’t want this to come off as bragging, I only bring it up because if anyone has any questions about how I build my credit or the different aspects of my score I’m more than willing to help others. You can hit them up by email: PINNACLECREDITSPECIALIST@GMAIL.COM or call +1 (409) 331 2269. Don’t fail to let him know Aaron referred you to him.

  • charityjonathan210b4ba46d523184fed

    Jul 11, 2025

    Victim of an NFT Scam or Cryptocurrency Investment Fraud? Take Action Now – Schedule a Consultation with APEX INTERVENTION LTD At APEX Intervention Limited, we are a trusted private investigation and funds recovery firm. As financial regulators and ethical hackers, we specialize in: Cryptocurrency scam recovery NFT scam investigations Fraudulent investment schemes Recovery scam exposure We operate with transparency: Let us show you the true art and integrity of ethical hacking. Our team is fully equipped with industry-leading recovery tools to handle your case from start to finish. Reach out to our team today: Email: info@apexintervention.online WhatsApp: +1 (365) 740-5227 Website: https://apex-intervention.online Your recovery starts with the right team. Choose APEX Intervention Limited – trusted, transparent, and relentless.

  • donaldspringer85879336ef456e64e48

    Jul 13, 2025

    Hello, so I’ve been trying to rebuild my credit. On May 18th I paid off a capital one card and my TransUnion vantage score dropped 35 points to 548. Didn’t see an increase. The next week I paid off another card (fortiva) and I saw my Equifax score drop 40 points down to 538. I’m using credit karma and when I’ve seen those drops, under recent activity is where it shows the CC balance decreased. 5 total credit cards. 2 paid off and 3 at 100% utilization. I do have 3 collections on file and chapter 7 BK. Last collection I’ve paid off with deletion, the score didn’t move yet my cards are dropping my scores. Does this make sense? This really frustrated me. I worked my butt off and even though I’m making progress in paying off the debt, it doesn’t seem it is benefiting my score. In contrast I read about PINNACLE CREDIT SPECIALIST on Quora and Medium and I didn’t hesitate to contact him, to my greatest surprise, when I logged into Credit Karma this morning and it stated that a public record has been removed. I found it strange, so I looked further, and it was indeed my Chapter 7 BK that had been removed. I did not argue. It was just removed from TransUnion by Pinnacle Credit Specialist. My credit score has been increased to 800+ across the three credit bureaus. This is what I can only describe as a Miracle! All thanks to Pinnacle Credit Specialist, the savior I met last month. You can reach out to him by email: PINNACLECREDITSPECIALIST@GMAIL.COM or call +1 (409) 331-2269. UPDATE: I just checked myFICO TransUnion and the bankruptcy is completely removed.

  • Marcus Henderson

    Jul 16, 2025

    Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: Capitalcryptorecover@zohomail.com Phone CALL/Text Number: +1 (336) 390-6684 Email: Recovercapital@cyberservices.com Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • Marcus Henderson

    Jul 16, 2025

    Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: Capitalcryptorecover@zohomail.com Phone CALL/Text Number: +1 (336) 390-6684 Email: Recovercapital@cyberservices.com Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • Elizabeth

    Jul 24, 2025

    HOW I GOT MY HUSBAND BACK WITH THE HELP OF PRIEST ZION CONTACT ON WHATS_APP NUMBER +2349129421831 This is my testimony about the good work of priest zion who helped me … I’m Elizabeth from North Carolina, USA. And am sorry for putting this on net but i will have to, by this world best spell caster that brought back my husband who left me out for past 3 years, i eventually met this man on a blog site posting by one of is client for help, i explained everything to him and he told me about a spell caster that he had heard about and he gave me an email address to write to the spell caster to tell him my problems. In just 1 days, my husband was back to me. I just want to say thank you to this truthful and sincere spell caster, sir all you told me have come to pass and thank you sir. Please I want to tell everyone who is looking for any solution to their problem, I advise you to kindly consult this spell caster, he is real,he is powerful and whatever the spell caster tells is what will happen, because all what the spell caster told me came to pass. You can kindly contact him on: his email address is leading.light.solution1@gmail.com or directly on whats-app +2349129421831 https://leadinglightsoluti.wixsite.com/my-site-1

  • Elizabeth Rush

    Jul 24, 2025

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: Recovercapital@cyberservices.com Contact Telegram: @Capitalcryptorecover His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • rubmonica805c3eb60f66b8a407f

    Aug 07, 2025

    HIRE THE BEST CRYPTO // BITCOIN RECOVERY EXPERT // THE HACK ANGELS I Can't Access My USDT? Account, Bitcoin Recovery Getting Back Lost Or Stolen Funds? How Do I Recover Crypto From A Scammer? If you’re in need of a reliable crypto asset and fund recovery service. Reach out to THE HACK ANGELS RECOVERY EXPERT WhatsApp +1(520)2 0 0-2 3 2 0) Email at support@thehackangels.com Website at www.thehackangels.com I can't get over how excited I am to have discovered THE HACK ANGELS RECOVERY EXPERT through a friend. After falling prey to a cryptocurrency fraud. However, Thanks to THE HACK ANGELS RECOVERY EXPERT I was able to regain a portion of my hard-earned funds. If you're feeling overwhelmed and frustrated by the loss of your hard-earned money, fear not! Contact THE HACK ANGELS RECOVERY EXPERT today and let him work his magic in recovering what is rightfully yours. As a professional in the field of online security and data recovery, I must say this, the most reliable and dependable recovery agent available online is THE HACK ANGELS RECOVERY EXPERT. With years of experience and a proven track record of successful recoveries. I can't express how grateful I am for their outstanding assistance on my case.

  • rubmonica805c3eb60f66b8a407f

    Aug 07, 2025

    HIRE THE BEST CRYPTO // BITCOIN RECOVERY EXPERT // THE HACK ANGELS I Can't Access My USDT? Account, Bitcoin Recovery Getting Back Lost Or Stolen Funds? How Do I Recover Crypto From A Scammer? If you’re in need of a reliable crypto asset and fund recovery service. Reach out to THE HACK ANGELS RECOVERY EXPERT WhatsApp +1(520)2 0 0-2 3 2 0) Email at support@thehackangels.com Website at www.thehackangels.com I can't get over how excited I am to have discovered THE HACK ANGELS RECOVERY EXPERT through a friend. After falling prey to a cryptocurrency fraud. However, Thanks to THE HACK ANGELS RECOVERY EXPERT I was able to regain a portion of my hard-earned funds. If you're feeling overwhelmed and frustrated by the loss of your hard-earned money, fear not! Contact THE HACK ANGELS RECOVERY EXPERT today and let him work his magic in recovering what is rightfully yours. As a professional in the field of online security and data recovery, I must say this, the most reliable and dependable recovery agent available online is THE HACK ANGELS RECOVERY EXPERT. With years of experience and a proven track record of successful recoveries. I can't express how grateful I am for their outstanding assistance on my case.

  • Patricia Lovick

    Aug 07, 2025

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. You can reach them via email at Capitalcryptorecover@zohomail.com OR Call/Text Number +1 (336)390-6684