Introduction to Networks

• Graph

  A collection of vertices (nodes) connected by edges.
• Network

  A real-world application of a graph, often involving flow or connections.
• Vertex / Node


  A point in a graph representing an object or position.
• Edge

  A line connecting two vertices, showing a relationship or link.
• Loop

  An edge that connects a vertex to itself. Counted as 2 edges.
• Degree (of a vertex)

  The number of edges connected to a vertex (loops count twice).
• Directed edge / graph

  Edges have no direction; connections go both ways.
• Weights / Weighted graph

  Edges have values (weights) representing cost, distance, etc.
• Connected

  Every vertex can be reached from others.
• Disconnected

  Some vertices cannot be reached from others.
• Simple graph

  A graph with no loops or multiple edges between the same vertices.
• Not simple graph

  A graph that contains loops and/or multiple edges between the same vertices.
• Isomorphic graphs

  Two graphs that have the same number of nodes and edges, and the same connectivity between nodes, even if the node and edge labels differ.
• Bridges

  Edges in a network (or graph) whose removal would disconnect the network into two or more separate components.
• Is this a simple or not simple graph?

  Not simple graph; loops, multiple edges connecting to the same vertex.