scrapbook
  • "Unorganized" Notes
  • The Best Public Datasets for Machine Learning and Data Science
  • Practice Coding
  • plaid-API project
  • Biotech
    • Machine Learning vs. Deep Learning
  • Machine Learning for Computer Graphics
  • Books (on GitHub)
  • Ideas/Thoughts
  • Ziva for feature animation: Stylized simulation and machine learning-ready workflows
  • Tools
  • 🪶math
    • Papers
    • Math for ML (coursera)
      • Linear Algebra
        • Wk1
        • Wk2
        • Wk3
        • Wk4
        • Wk5
      • Multivariate Calculus
    • Improving your Algorithms & Data Structure Skills
    • Algorithms
    • Algorithms (MIT)
      • Lecture 1: Algorithmic Thinking, Peak Finding
    • Algorithms (khan academy)
      • Binary Search
      • Asymptotic notation
      • Sorting
      • Insertion sort
      • Recursion
      • Solve Hanoi recursively
      • Merge Sort
      • Representing graphs
      • The breadth-first search algorithm
      • Breadth First Search in JavaScript
      • Breadth-first vs Depth-first Tree Traversal in Javascript
    • Algorithms (udacity)
      • Social Network
    • Udacity
      • Linear Algebra Refresher /w Python
    • math-notes
      • functions
      • differential calculus
      • derivative
      • extras
      • Exponentials & logarithms
      • Trigonometry
    • Probability (MIT)
      • Unit 1
        • Probability Models and Axioms
        • Mathematical background: Sets; sequences, limits, and series; (un)countable sets.
    • Statistics and probability (khan academy)
      • Analyzing categorical data
      • Describing and comparing distributions
      • Outliers Definition
      • Mean Absolute Deviation (MAD)
      • Modeling data distribution
      • Exploring bivariate numerical data
      • Study Design
      • Probability
      • Counting, permutations, and combinations
      • Binomial variables
        • Binomial Distribution
        • Binomial mean and standard deviation formulas
        • Geometric random variable
      • Central Limit Theorem
      • Significance Tests (hypothesis testing)
    • Statistics (hackerrank)
      • Mean, Medium, Mode
      • Weighted Mean
      • Quartiles
      • Standard Deviation
      • Basic Probability
      • Conditional Probability
      • Permutations & Combinations
      • Binomial Distribution
      • Negative Binomial
      • Poisson Distribution
      • Normal Distribution
      • Central Limit Theorem
      • Important Concepts in Bayesian Statistics
  • 📽️PRODUCT
    • Product Strategy
    • Product Design
    • Product Development
    • Product Launch
  • 👨‍💻coding
    • of any interest
    • Maya API
      • Python API
    • Python
      • Understanding Class Inheritance in Python 3
      • 100+ Python challenging programming exercises
      • coding
      • Iterables vs. Iterators vs. Generators
      • Generator Expression
      • Stacks (LIFO) / Queues (FIFO)
      • What does -1 mean in numpy reshape?
      • Fold Left and Right in Python
      • Flatten a nested list of lists
      • Flatten a nested dictionary
      • Traverse A Tree
      • How to Implement Breadth-First Search
      • Breadth First Search
        • Level Order Tree Traversal
        • Breadth First Search or BFS for a Graph
        • BFS for Disconnected Graph
      • Trees and Tree Algorithms
      • Graph and its representations
      • Graph Data Structure Interview Questions
      • Graphs in Python
      • GitHub Repo's
    • Python in CG Production
    • GLSL/HLSL Shading programming
    • Deep Learning Specialization
      • Neural Networks and Deep Learning
      • Untitled
      • Untitled
      • Untitled
    • TensorFlow for AI, ML, and DL
      • Google ML Crash Course
      • TensorFlow C++ API
      • TensorFlow - coursera
      • Notes
      • An Introduction to different Types of Convolutions in Deep Learning
      • One by One [ 1 x 1 ] Convolution - counter-intuitively useful
      • SqueezeNet
      • Deep Compression
      • An Overview of ResNet and its Variants
      • Introducing capsule networks
      • What is a CapsNet or Capsule Network?
      • Xception
      • TensorFlow Eager
    • GitHub
      • Project README
    • Agile - User Stories
    • The Open-Source Data Science Masters
    • Coding Challenge Websites
    • Coding Interview
      • leetcode python
      • Data Structures
        • Arrays
        • Linked List
        • Hash Tables
        • Trees: Basic
        • Heaps, Stacks, Queues
        • Graphs
          • Shortest Path
      • Sorting & Searching
        • Depth-First Search & Breadth-First Search
        • Backtracking
        • Sorting
      • Dynamic Programming
        • Dynamic Programming: Basic
        • Dynamic Programming: Advanced
    • spaCy
    • Pandas
    • Python Packages
    • Julia
      • jupyter
    • macos
    • CPP
      • Debugging
      • Overview of memory management problems
      • What are lvalues and rvalues?
      • The Rule of Five
      • Concurrency
      • Avoiding Data Races
      • Mutex
      • The Monitor Object Pattern
      • Lambdas
      • Maya C++ API Programming Tips
      • How can I read and parse CSV files in C++?
      • Cpp NumPy
    • Advanced Machine Learning
      • Wk 1
      • Untitled
      • Untitled
      • Untitled
      • Untitled
  • data science
    • Resources
    • Tensorflow C++
    • Computerphile
      • Big Data
    • Google ML Crash Course
    • Kaggle
      • Data Versioning
      • The Basics of Rest APIs
      • How to Make an API
      • How to deploying your API
    • Jupiter Notebook Tips & Tricks
      • Jupyter
    • Image Datasets Notes
    • DS Cheatsheets
      • Websites & Blogs
      • Q&A
      • Strata
      • Data Visualisation
      • Matplotlib etc
      • Keras
      • Spark
      • Probability
      • Machine Learning
        • Fast Computation of AUC-ROC score
    • Data Visualisation
    • fast.ai
      • deep learning
      • How to work with Jupyter Notebook on a remote machine (Linux)
      • Up and Running With Fast.ai and Docker
      • AWS
    • Data Scientist
    • ML for Beginners (Video)
    • ML Mastery
      • Machine Learning Algorithms
      • Deep Learning With Python
    • Linear algebra cheat sheet for deep learning
    • DL_ML_Resources
    • Awesome Machine Learning
    • web scraping
    • SQL Style Guide
    • SQL - Tips & Tricks
  • 💡Ideas & Thoughts
    • Outdoors
    • Blog
      • markdown
      • How to survive your first day as an On-set VFX Supervisor
    • Book Recommendations by Demi Lee
  • career
    • Skills
    • learn.co
      • SQL
      • Distribution
      • Hypothesis Testing Glossary
      • Hypothesis Tests
      • Hypothesis & AB Testing
      • Combinatorics Continued and Maximum Likelihood Estimation
      • Bayesian Classification
      • Resampling and Monte Carlo Simulation
      • Extensions To Linear Models
      • Time Series
      • Distance Metrics
      • Graph Theory
      • Logistic Regression
      • MLE (Maximum Likelihood Estimation)
      • Gradient Descent
      • Decision Trees
      • Ensemble Methods
      • Spark
      • Machine Learning
      • Deep Learning
        • Backpropagation - math notation
        • PRACTICE DATASETS
        • Big Data
      • Deep Learning Resources
      • DL Datasets
      • DL Tutorials
      • Keras
      • Word2Vec
        • Word2Vec Tutorial Part 1 - The Skip-Gram Model
        • Word2Vec Tutorial Part 2 - Negative Sampling
        • An Intuitive Explanation of Convolutional Neural Networks
      • Mod 4 Project
        • Presentation
      • Mod 5 Project
      • Capstone Project Notes
        • Streaming large training and test files into Tensorflow's DNNClassifier
    • Carrier Prep
      • The Job Search
        • Building a Strong Job Search Foundation
        • Key Traits of Successful Job Seekers
        • Your Job Search Mindset
        • Confidence
        • Job Search Action Plan
        • CSC Weekly Activity
        • Managing Your Job Search
      • Your Online Presence
        • GitHub
      • Building Your Resume
        • Writing Your Resume Summary
        • Technical Experience
      • Effective Networking
        • 30 Second Elevator Pitch
        • Leveraging Your Network
        • Building an Online Network
        • Linkedin For Research And Networking
        • Building An In-Person Network
        • Opening The Line Of Communication
      • Applying to Jobs
        • Applying To Jobs Online
        • Cover Letters
      • Interviewing
        • Networking Coffees vs Formal Interviews
        • The Coffee Meeting/ Informational Interview
        • Communicating With Recruiters And HR Professional
        • Research Before an Interview
        • Preparing Questions for Interviews
        • Phone And Video/Virtual Interviews
        • Cultural/HR Interview Questions
        • The Salary Question
        • Talking About Apps/Projects You Built
        • Sending Thank You's After an Interview
      • Technical Interviewing
        • Technical Interviewing Formats
        • Code Challenge Best Practices
        • Technical Interviewing Resources
      • Communication
        • Following Up
        • When You Haven't Heard From an Employer
      • Job Offers
        • Approaching Salary Negotiations
      • Staying Current in the Tech Industry
      • Module 6 Post Work
      • Interview Prep
  • projects
    • Text Classification
    • TERRA-REF
    • saildrone
  • Computer Graphics
  • AI/ML
  • 3deeplearning
    • Fast and Deep Deformation Approximations
    • Compress and Denoise MoCap with Autoencoders
    • ‘Fast and Deep Deformation Approximations’ Implementation
    • Running a NeuralNet live in Maya in a Python DG Node
    • Implement a Substance like Normal Map Generator with a Convolutional Network
    • Deploying Neural Nets to the Maya C++ API
  • Tools/Plugins
  • AR/VR
  • Game Engine
  • Rigging
    • Deformer Ideas
    • Research
    • brave rabbit
    • Useful Rigging Links
  • Maya
    • Optimizing Node Graph for Parallel Evaluation
  • Houdini
    • Stuff
    • Popular Built-in VEX Attributes (Global Variables)
Powered by GitBook
On this page
  • Characteristics
  • Why do I need to know about this?
  • Additional Resources
  • Networkx
  • Community Detection
  • Ego Networks
  1. career
  2. learn.co

Graph Theory

PreviousDistance MetricsNextLogistic Regression

Last updated 6 years ago

Characteristics

Absent

Present

Weights

Unweighted

Weighted

Directionality

Undirected

Directed

Why do I need to know about this?

Graph is a data structure which is used extensively in our real-life.

  • Social Networks: Each user is represented as a node and all their activities,suggestion and friend list are represented as an edge between the nodes.

  • Google Maps: Various locations are represented as vertices or nodes and the roads are represented as edges and graph theory is used to find shortest path between two nodes.

  • Recommendations on e-commerce websites: The “Recommendations for you” section on various e-commerce websites uses graph theory to recommend items of similar type to user’s choice.

  • Graph theory is also used to study molecules in chemistry and physics.

Additional Resources

Networkx

The notion of centrality helps us identify Which nodes are most 'central' in a given network. Definition of 'central' varies by context/purpose of the analysis and situation. It could be based of number of connections or with a discrimination between incoming and outgoing connections from a node. A local measure for calculating centrality on these lines is the "Degree" of a node.

Degree Centrality

The degree of a node is the number of other nodes to which it is connected.

Closeness Centrality

Closeness Centrality measures how many "hops" a node would take to reach every other node in a network (taking the shortest path). It can be informally thought as 'average distance' to all other nodes. This "Far-ness" is then transformed into "nearness" as the reciprocal of farness. That is, nearness = one divided by farness. "Nearness" can be further standardized by norming against the minimum possible nearness for a graph of the same size and connection.

Betweeness Centrality

Betweenness centrality measures the number of times a node acts as a bridge along the shortest path between two other nodes. Here nodes that have a high probability to occur on a randomly chosen shortest path between two randomly chosen nodes have a high betweenness.

A node is high in eigenvector centrality if it is connected to many other nodes who are themselves well connected. Eigenvector centrality for each node is simply calculated as the proportional eigenvector values of the eigenvector with the largest eigenvalue. Following image shows you a quick comparison between degree and eigenvector centrality. Here node A is connected to more well connected nodes than B and hence shows a higher Eigenvector centrality, although the degree of B is higher than A.

Community Detection

Ego Networks

Network Centrality

CB(v)=∑s,t∈Vσ(s,t∣v)σ(s,t)C_B(v) =\sum_{s,t \in V} \frac{\sigma(s, t|v)}{\sigma(s, t)}CB​(v)=∑s,t∈V​σ(s,t)σ(s,t∣v)​

where σ(s,t){\sigma(s, t)}σ(s,t) is total number of shortest paths from node s{s}s to node t{t}t and σ(s,t∣v){\sigma(s, t|v)}σ(s,t∣v) is the number of those paths that pass through v{v}v.

Eigenvector Centrality

, which involves some matrix algebra. We shall use networkx's built in method to calculate this for now.

Graph Theory Basics
A Gentle Introduction to Graph Theory
¶
¶
Visit here to get a deep dive in the underlying maths