7    VisuAlgo.net / /graphds Login Undirected/Unweighted U/W D/U D/W
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A graph is made up of 'vertices' (or 'nodes') and 'edges' (or 'lines') that connect those vertices. A graph may be undirected (or bidirectional), meaning that there is no distinction between the two vertices associated with each edge, or its edges may be directed from one vertex to another but not necessarily in the other direction. A graph can be weighted by assigning a weight to each edge, which represent numerical values associated with that connection, or a graph can be unweighted (either all edges have unit weight 1 or all edges have the same constant weight).


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To toggle between the graph drawing modes, select the respective header. We have:

  1. U/U = Undirected/Unweighted (default),
  2. U/W = Undirected/Weighted,
  3. D/U = Directed/Unweighted, and
  4. D/W = Directed/Weighted.
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View the graph here!


You can also draw a graph directly here:

  1. Click on empty space to add vertex,
  2. Click a vertex, hold, drag the drawn edge to another vertex, and drop it there to add an edge,
  3. Select a vertex/edge and press 'Delete' key to delete that vertex/edge,
  4. Select an edge and press 'Enter' to change the weight of that edge [0..99],
  5. Press and hold 'Ctrl', then you can click and drag a vertex around.
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All example graphs can be found here. You can further modify these example graphs to suit your needs.

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Adjacency matrix is a square matrix where the entry A[i][j] shows the edge's weight from vertex i to vertex j. An 'x' means that the vertex does not exist. An Adjacency Matrix requires a big space complexity of O(V2).


Adjacency List is a list showing the set of neighbors of each vertex (usually in increasing vertex number, as shown in this visualization). Adjacency List requires an O(V+E) space, much more efficient than Adjacency Matrix and usually the default graph data structure for most cases.


Edge list is a collection of edges with both connecting vertices and their weights. Usually, these edges are sorted by increasing weight, e.g. part of Kruskal's algorithm for Minimum Spanning Tree (MST) problem. However in this visualization, we sort the edges based on increasing v1 and if ties, by increasing v2. Bidirectional edges in undirected graph are only listed once. Bidirectional edges in directed graph are listed twice.

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Tree, Complete, Bipartite, Directed Acyclic Graph (DAG) are properties of special graphs. As you modify the graph above, these properties are checked instantly.

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• Tree? No • Complete? No • Bipartite? No • DAG? No
Adjacency Matrix
012
0010
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2010
Adjacency List
0: 1
1: 02
2: 1
Edge List
0: 01
1: 12

CP3 Fig 2.4

CP3 Fig 4.10

CP3 Fig 4.4

CP3 Fig 4.26B*

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About Team Terms of use

About

VisuAlgo was conceptualised in 2011 by Dr Steven Halim as a tool to help his students better understand data structures and algorithms, by allowing them to learn the basics on their own and at their own pace.

VisuAlgo contains many advanced algorithms that are discussed in Dr Steven Halim's book ('Competitive Programming', co-authored with his brother Dr Felix Halim) and beyond. Today, some of these advanced algorithms visualization/animation can only be found in VisuAlgo.

Though specifically designed for National University of Singapore (NUS) students taking various data structure and algorithm classes (e.g. CS1010, CS1020, CS2010, CS2020, CS3230, and CS3230), as advocators of online learning, we hope that curious minds around the world will find these visualisations useful too.

VisuAlgo is not designed to work well on small touch screens (e.g. smartphones) from the outset due to the need to cater for many complex algorithm visualizations that require lots of pixels and click-and-drag gestures for interaction. The minimum screen resolution for a respectable user experience is 1024x768 and only the landing page is relatively mobile-friendly.

VisuAlgo is an ongoing project and more complex visualisations are still being developed.

The most exciting development is the automated question generator and verifier (the online quiz system) that allows students to test their knowledge of basic data structures and algorithms. The questions are randomly generated via some rules and students' answers are instantly and automatically graded upon submission to our grading server. This online quiz system, when it is adopted by more CS instructors worldwide, should technically eliminate manual basic data structure and algorithm questions from typical Computer Science examinations in many Universities. By setting a small (but non-zero) weightage on passing the online quiz, a CS instructor can (significantly) increase his/her students mastery on these basic questions as the students have virtually infinite number of training questions that can be verified instantly before they take the online quiz. The training mode currently contains questions for 12 visualization modules. We will soon add the remaining 8 visualization modules so that every visualization module in VisuAlgo have online quiz component.

Another active branch of development is the internationalization sub-project of VisuAlgo. We want to prepare a database of CS terminologies for all English text that ever appear in VisuAlgo system. This is a big task and requires crowdsourcing. Once the system is ready, we will invite VisuAlgo visitors to contribute, especially if you are not a native English speaker. Currently, we have also written public notes about VisuAlgo in various languages: zh, id, kr, vn, th.

Team

Project Leader & Advisor (Jul 2011-present)
Dr Steven Halim, Senior Lecturer, School of Computing (SoC), National University of Singapore (NUS)
Dr Felix Halim, Software Engineer, Google (Mountain View)

Undergraduate Student Researchers 1 (Jul 2011-Apr 2012)
Koh Zi Chun, Victor Loh Bo Huai

Final Year Project/UROP students 1 (Jul 2012-Dec 2013)
Phan Thi Quynh Trang, Peter Phandi, Albert Millardo Tjindradinata, Nguyen Hoang Duy

Final Year Project/UROP students 2 (Jun 2013-Apr 2014)
Rose Marie Tan Zhao Yun, Ivan Reinaldo

Undergraduate Student Researchers 2 (May 2014-Jul 2014)
Jonathan Irvin Gunawan, Nathan Azaria, Ian Leow Tze Wei, Nguyen Viet Dung, Nguyen Khac Tung, Steven Kester Yuwono, Cao Shengze, Mohan Jishnu

Final Year Project/UROP students 3 (Jun 2014-Apr 2015)
Erin Teo Yi Ling, Wang Zi

Final Year Project/UROP students 4 (Jun 2016-Dec 2017)
Truong Ngoc Khanh, John Kevin Tjahjadi, Gabriella Michelle, Muhammad Rais Fathin Mudzakir

List of translators who have contributed ≥100 translations can be found at statistics page.

Acknowledgements
This project is made possible by the generous Teaching Enhancement Grant from NUS Centre for Development of Teaching and Learning (CDTL).

Terms of use

VisuAlgo is free of charge for Computer Science community on earth. If you like VisuAlgo, the only payment that we ask of you is for you to tell the existence of VisuAlgo to other Computer Science students/instructors that you know =) via Facebook, Twitter, course webpage, blog review, email, etc.

If you are a data structure and algorithm student/instructor, you are allowed to use this website directly for your classes. If you take screen shots (videos) from this website, you can use the screen shots (videos) elsewhere as long as you cite the URL of this website (http://visualgo.net) and/or list of publications below as reference. However, you are NOT allowed to download VisuAlgo (client-side) files and host it on your own website as it is plagiarism. As of now, we do NOT allow other people to fork this project and create variants of VisuAlgo. Using the offline copy of (client-side) VisuAlgo for your personal usage is fine.

Note that VisuAlgo's online quiz component is by nature has heavy server-side component and there is no easy way to save the server-side scripts and databases locally. Currently, the general public can only use the 'training mode' to access these online quiz system. Currently the 'test mode' is a more controlled environment for using these randomly generated questions and automatic verification for a real examination in NUS. Other interested CS instructor should contact Steven if you want to try such 'test mode'.

List of Publications

This work has been presented briefly at the CLI Workshop at the ACM ICPC World Finals 2012 (Poland, Warsaw) and at the IOI Conference at IOI 2012 (Sirmione-Montichiari, Italy). You can click this link to read our 2012 paper about this system (it was not yet called VisuAlgo back in 2012).

This work is done mostly by my past students. The most recent final reports are here: Erin, Wang Zi, Rose, Ivan.

Bug Reports or Request for New Features

VisuAlgo is not a finished project. Dr Steven Halim is still actively improving VisuAlgo. If you are using VisuAlgo and spot a bug in any of our visualization page/online quiz tool or if you want to request for new features, please contact Dr Steven Halim. His contact is the concatenation of his name and add gmail dot com.