These slides are based on those developed by Michael Böhlen for this course. if a graph is undirected, we represent an edge between by two pairs (u,v) . E and (v,u) u and v . Connected component – maximal connected subgraph. Example: …

Graph representations store information about which vertices are adjacent, and how the edges between the vertices are. Graph representations are slightly different if the edges are directed or weighted. Two vertices are adjacent, or neighbors, if there is an edge between them.

Mar 19, 2025 · Adjacency Matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. An adjacency matrix is a simple and straightforward way to represent graphs and is …

Nov 7, 2024 · An adjacency list is a data structure used to represent a graph where each node in the graph stores a list of its neighboring vertices.

Oct 5, 2024 · A Graph is a non-linear data structure consisting of nodes and edges. The nodes are sometimes also referred to as vertices and the edges are lines or arcs that connect any two nodes in the graph. The basic properties of a graph include: Vertices (nodes): The points where edges meet in a graph are kn

Adjacency: A vertex is said to be adjacent to another vertex if there is an edge connecting them. Vertices 2 and 3 are not adjacent because there is no edge between them. Path: A sequence of edges that allows you to go from vertex A to vertex B is called a path. 0-1, 1-2 and 0-2 are paths from vertex 0 to vertex 2.

Graph ADT Functions: - insertVertex(K key); - insertEdge(Vertex v1, Vertex v2, K key); - removeVertex(Vertex v); - removeEdge(Vertex v1, Vertex v2); - getEdges(Vertex v); - areAdjacent(Vertex v1, Vertex v2); - origin(Edge e); - destination(Edge e); Data: - Vertices - Edges - Some data structure maintaining the structure between vertices and edges.

There are many ways to store graph information into a graph data structure. In this visualization, we show three graph data structures: Adjacency Matrix, Adjacency List, and Edge List — each with its own strengths and weaknesses.

Data Structures for Graphs - Explore the various data structures used in graph theory, including adjacency lists, adjacency matrices, and more. Understand their applications and efficiency.

How will the adjacency matrix vary for an undirected graph? How can we adapt the representation for weighted graphs? Now we’ll implement some useful and non-trivial algorithms! Why do we perform topological sorts only on DAGs? Is there always a unique answer? Do some DAGs have exactly 1 answer? 417 XYZ Removed? In-degree: Running time?