Gain insights into key graph algorithms, including depth-first search, shortest paths, and flow networks. Explore their applications and foundational role in advanced computing disciplines.

This technology-agnostic course will teach you about many classical graph algorithms essential for a well-rounded software engineer. 

You will begin with an introduction to the running-time analysis of algorithms and the representation and structure of graphs. You’ll cover the depth-first search algorithm and its many applications, like detecting cycles, topological sorting, and identifying cut-vertices and strongly connected components. You will then cover algorithms for finding shortest paths and minimum spanning trees. You’ll also learn about the Ford-Fulkerson algorithm and its use in finding a maximum flow and minimum cut in networks. Moreover, you will adapt it to find maximum matchings and minimum vertex covers in bipartite graphs. Finally, you will learn about the Gale-Shapley algorithm for finding stable matchings.

The material in this course serves as a basis for other advanced algorithms, like parallel and distributed algorithms, and has many diverse applications in other computing disciplines.

Mastering Graph Algorithms

# Vertex and edge attributes

One of the things deeply ingrained in every computer science student is that _objects have properties_. So, if we put on our object-orientation hat, it’s clear that graphs are objects and so are vertices and edges. 


The graph representation chosen for an application can be extended to store additional information for the vertices and edges. In some cases, it may be a good idea to store the information in a second data structure (such as a two-dimensional array) with a structure similar to an adjacency matrix. This is especially true when constant time retrieval of information is required against individual edges.

The information stored on vertices and edges can be used to accomplish many things algorithmically.

# Weighted graphs

A **weighted graph** is a graph that has a real number associated with each edge. This real number may represent some kind of cost, quantity, or score. 

Of course, in computing contexts, the weight cannot be an irrational number. So, in most applications, it typically turns up as an integer or a rational number. 



Learn about the need for weighted graphs.

Introduction

Review: Asymptotic Notation and Math Prerequisites

Working with Graphs

Depth-First Search and Applications

Prelude: Shortest Paths

Single-source Shortest Paths in Weighted Digraphs

All Pairs Shortest Paths

Minimum Spanning Tree

Flows

Matchings and Vertex Covers

Conclusion

Use Simulated Annealing for the Traveling Salesman Problem

Weighted Graphs

Vertex and edge attributes