reading-notes

Graphs

A graph is a non-linear data structure that can be looked at as a collection of vertices (or nodes) potentially connected by line segments named edges.

Common terminology used when working with Graphs

• Vertex - A vertex, also called a “node”, is a data object that can have zero or more adjacent vertices.
• Edge - An edge is a connection between two nodes.
• Neighbor - The neighbors of a node are its adjacent nodes, i.e., are connected via an edge.
• Degree - The degree of a vertex is the number of edges connected to that vertex.

Undirected Graphs

An Undirected Graph is a graph where each edge is undirected or bi-directional. This means that the undirected graph does not move in any direction.

For example, in the graph below, Node C is connected to Node A, Node E and Node B. There are no “directions” given to point to specific vertices. The connection is bi-directional.

Directed Graphs

A Directed Graph also called a Digraph is a graph where every edge is directed.

Unlike an undirected graph, a Digraph has direction. Each node is directed at another node with a specific requirement of what node should be referenced next.

Compare the visual below with the undirected graph above. Can you see the difference? The Digraph has arrows pointing to specific nodes.

Complete vs Connected vs Disconnected

There are many different types of graphs. This depends on how connected the graphs are to other node/vertices.

The three different types are completed, connected, and disconnected.

Acyclic vs Cyclic

Acyclic Graph

An acyclic graph is a directed graph without cycles.

A cycle is when a node can be traversed through and potentially end up back at itself.

Cyclic Graphs

A Cyclic graph is a graph that has cycles.

A cycle is defined as a path of a positive length that starts and ends at the same vertex.

Graph Representation

• Adjacency Matrix
• Adjacency List

Adjacency Matrix

An Adjacency matrix is represented through a 2-dimensional array. If there are n vertices, then we are looking at an n x n Boolean matrix

Each Row and column represents each vertex of the data structure. The elements of both the column and the row must add up to 1 if there is an edge that connects the two, or zero if there isn’t a connection.

Adjacency List

An adjacency list is the most common way to represent graphs. An adjacency list is a collection of linked lists or array that lists all of the other vertices that are connected.

Adjacency lists make it easy to view if one vertices connects to another.

Weighted Graphs

A weighted graph is a graph with numbers assigned to its edges. These numbers are called weights.

Real World Uses of Graphs

• GPS and Mapping
• Driving Directions
• Social Networks
• Airline Traffic
• Netflix uses graphs for suggestions of products