Graph fundamentals
A graph is a set of vertices connected to each other. It has at least one line joining a set of two vertices with no vertex connecting itself. Some basic terms are:
- point
- line
- vertex
- edge
- degree of vertices
- properties of graphs
- etc.
Point
A point is a particular position in a one-dimensional, two-dimensional, or three-dimensional space. For better understanding, a point can be denoted by a letter and represented with a dot.
For example
The graph on the right shows the dot as a point named ‘a’.
Line
A line is a connection between two points. It can be represented with a solid line
For example:
The graph on the right shows points ‘a’ and ‘b’. The link between these two points is called a line.
graph = { "a" : ["c"],"b" : ["c", "e"],"c" : ["a", "b", "d", "e"],"d" : ["c"],"e" : ["c", "b"],"f" : []}def generate_edges(graph):edges = []for node in graph:for neighbour in graph[node]:edges.append((node, neighbour))return edgesprint(generate_edges(graph))
Vertex
A vertex is a point where multiple lines meet. It is also called a node. Similar to points, a vertex is denoted by a letter.
Edge
An edge is a mathematical term used for a line that connects two vertices. Many edges can be formed from a single vertex. However, without a vertex, an edge cannot be formed – there must be a starting vertex and an ending vertex for an edge.
Graph
A graph, G , is defined as G = (V, E) – where V is a set of all vertices and E is a set of all edges in the graph.
Loop
In a graph, if an edge is drawn from the vertex to itself, it is called a loop. In the illustration, V is a vertex whose edge, (V, V), is forming a loop.
For example
Turtle is a built-in module in Python. It provides you with a drawing canvas (cardboard) and turtle (pen). To draw something on the canvas, we need to move the turtle (pen). To move the turtle, there are some functions:
forward()backward()left()right()
import turtlet = turtle.Turtle()t.right(90)t.forward(80)t.left(90)t.forward(80)t.left(90)t.forward(80)t.left(90)t.forward(80)
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