Graph Mining: Introducing Graphs: Learn by finding answers to the following questions?
Questions
What is a Graph?
Give an example of a Graph?
What are the different Types of Graphs? i.e. Try to give some examples of different ways how Graphs are classified?
What is a directed Graph?
What is an undirected Graph?
What are Labeled Graphs?
What are Weighted Graphs?
What are the unweighted Graphs?
What are the Bipartite Graphs?
What is a Tree?
What is a Signed Graph?
What is a Looped Graph? i.e. What is a loop?
Compare Static and Time-evolving Graphs.
What is an Isomorphic Graph?
What does Isomorphism mean when it comes to Graphs?
What are different ways to represent Graphs? i.e. when implementing Graph Algorithms?
How to store a Graph data in programming languages?
Describe the Adjacency Matrix approach of Graph Representation.
Give a small example graph then represent it using the Adjacency Matrix approach of Graph Representation.
Represent the following Graph using Adjacency Matrix approach of Graph Representation
Edges: {0, 1} {0, 4} {1, 2} {1, 3} {1, 4} {2, 3} {3, 4}
What are the advantages/pros of the Adjacency Matrix Representation?
What are the disadvantages/cons of the Adjacency Matrix Representation?
Describe the Adjacency List approach of Graph Representation.
Give a small example graph then represent it using the Adjacency List approach of Graph Representation.
Represent the following Graph using Adjacency List approach of Graph Representation
Edges: {0, 1} {0, 4} {1, 2} {1, 3} {1, 4} {2, 3} {3, 4}
What are the advantages/pros of the Adjacency List Representation?
What are the disadvantages/cons of the Adjacency List Representation?
Describe the Adjacency Tensor approach of Graph Representation.
Give a small example graph then represent it using the Adjacency Tensor approach of Graph Representation.
Represent the following Graph using Adjacency Tensor approach of Graph Representation
Edges: {0, 1} {0, 4} {1, 2} {1, 3} {1, 4} {2, 3} {3, 4}
What are the advantages/pros of Adjacency Tensor Representation?
What are the disadvantages/cons of Adjacency Tensor Representation?
True or False? Adjacency Matrix is a 2D array of size V x V where V is the number of vertices in a graph.
Can the Adjacency Matrix represent weighted graphs?
How easy it is you think to represent graphs using Adjacency Matrix?
What is the complexity of removing an edge from Adjacency Matrix representation?
What is the complexity of queries such as whether there is an edge between vertex a and b for Adjacency Matrix representation?
What is the Space complexity for Adjacency Matrix representation? Use vertex count to represent.
What is the complexity of adding an edge from Adjacency Matrix representation?
For the Adjacency List approach, how many total lists are there? How many vertices each list can have at best?
For the Adjacency List approach, how many lists are there for one vertex?
How much Space does the Adjacency List approach take?
How many elements does an Adjacency list contain for an undirected graph? Represent using E = edge count. For the complete representation of the Graph.
Why the complete representation of an undirected Graph using Adjacency List will have 2|E| number of elements?
How many times does an edge appear in the complete representation of the Undirected Graph using the Adjacency List?
Why the complete representation of the Directed Graph using Adjacency List will have |E| number of elements?
How many times does an edge appear in the complete representation of the Directed Graph using the Adjacency List?
How many dimensions will an Adjacency Tensor have for Tensor? What is this for Dynamic Graphs?
Some Answers
What are the different Types of Graphs? i.e. Try to give some examples of different ways how Graphs are classified?
Ans: Undirected vs. Directed, Attributed/Labeled (e.g., vertex, edge) vs. Unlabeled, Weighted vs. Unweighted, General vs. Bipartite (Multipartite), Signed Graphs, Trees (no cycles), Simple vs. w/ loops vs. w/ multi-edges, Static vs. Time Evolving Graphs, Isomorphic Graphs
What are the different ways to represent Graphs? i.e. when implementing Graph Algorithms?
Ans: Static Graphs, Adjacency Matrix, Adjacency List, Dynamic Graphs, Adjacency 3D Tensor
Resources:
Graph mining - lesson 1 Introduction to graphs and networks Nathalie Vialaneix
http://www.nathalievialaneix.eu/teaching/m2se/M2SE-network_1.pdf
phpFox Features: Start your own Social Network
https://www.phpfox.com/features/
Bipartite graph
https://en.wikipedia.org/wiki/Bipartite_graph
Tree (data structure)
https://en.wikipedia.org/wiki/Tree_(data_structure)
Tree structure
https://en.wikipedia.org/wiki/Tree_structure
Signed graph
https://en.wikipedia.org/wiki/Signed_graph
Gene regulatory network
https://en.wikipedia.org/wiki/Gene_regulatory_network
Dynamic Influence Analysis in Evolving Networks (VLDB'16)
https://www.slideshare.net/todo314/dynamic-influence-analysis-in-evolving-networks-vldb16
Introduction to Graph Theory
https://www.csc2.ncsu.edu/faculty/nfsamato/practical-graph-mining-with-R/slides/ppt/Introduction_to_Graph_Theory.ppt
Graph and its representations
https://www.geeksforgeeks.org/graph-and-its-representations/
Representing graphs
https://www.khanacademy.org/computing/computer-science/algorithms/graph-representation/a/representing-graphs
https://www.geeksforgeeks.org/graph-and-its-representations/
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