Implementation: Graphs
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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.
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common terminology used when working with Graphs:
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Vertex - A vertex, also called a “node”, is a data object that can have zero or more adjacent vertices.
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Edge - An edge is a connection between two nodes.
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Neighbor - The neighbors of a node are its adjacent nodes, i.e., are connected via an edge.
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Degree - The degree of a vertex is the number of edges connected to that vertex.
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Directed vs Undirected
- 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.
- 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.
Complete vs Connected vs Disconnected
- A complete graph is when all nodes are connected to all other nodes.
- A connected graph is graph that has all of vertices/nodes have at least one edge.
- A disconnected graph is a graph where some vertices may not have edges.
Acyclic vs Cyclic
- 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.
Here is an example of 3 acyclic 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.
Here is an example of a two different cyclic graph:
Graph Representation
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We represent graphs through:
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Adjacency Matrix
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Adjacency List
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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.
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An adjacency list is a collection of linked lists or array that lists all of the other vertices that are connected.
Weighted Graphs
- A weighted graph is a graph with numbers assigned to its edges. These numbers are called weights.
