Computer Science: Graphs Overview

Graph Fundamentals

• A graph is a non-linear data structure in computer science, consisting of nodes and edges that connect them.
• Nodes, also known as vertices, are the points in a graph that are connected by edges.
• Edges are the connections between nodes, which can be directed or undirected.

Graph Representation

• Graphs can be represented using two main methods: adjacency matrix and adjacency list.
• An adjacency matrix is a square matrix where the entry in the ith row and jth column represents the number of edges between the ith and jth nodes.
• An adjacency list is a collection of unordered lists, each representing the nodes connected to a particular node.

Graph Types

• An undirected graph is a graph where the edges do not have a direction, meaning they can be traversed in both directions.
• A directed graph, also known as a digraph, is a graph where the edges have a direction, meaning they can only be traversed in one direction.
• A weighted graph is a graph where the edges have a weight or cost associated with them, which can be used to calculate the shortest path between nodes.

Graph Properties

• A cyclic graph is a graph that contains at least one cycle, which is a path that starts and ends at the same node.
• A connected graph is a graph where there is a path between every pair of nodes.
• A tree is a connected graph with no cycles, where every node is connected to every other node through a unique path.

Graph Complexity

• The space complexity of an adjacency matrix is O(n^2), where n is the number of nodes in the graph.

Test your understanding of the basic concepts, representations, and searching in computer science graphs. This quiz covers the abstract data type, undirected and directed graph concepts, and their implementation in the field of graph theory.