Niche overlap graphs in Ecology
A nice graph is a simple graph because no loops or multiple edges are needed in this model.
For example, the competition between species by a vertex. An undirected edge connects two vertices if the two species represented by these vertices compete (i.e., some of the food resources they use are the same).
In this graph, no multiple edges and no loops are used. The acquaintanceship graph of all people in people in the world has more than six billion vertices and probably more than one trillion edges.
A directed graph called an influence graph can be used to study group behavior. Each person of the group is represented by a vertex. There is a directed edge from vertex a to vertex b when the person represented by vertex a influences the person represented by vertex by vertex influences the person represented by vertex b. this graph does not contain loops and it does not contain multiple directed edges.
The Hollywood graph represents actors by vertices and connects two vertices when the actors represented by these vertices have acted together one a movie. This graph is a simple graph since its edges are undirected, it contains no loops.
A tournament where each team plays each other team exactly once is called a Round-Robin tournament. It can be modelled using directed graphs where each team is represented by a vertex. Note that (a,b) is an edge if team a beats team b. this graph is a sample containing no loops or multiple directed edges( because no two teams can play each other more than once). We see that team 5 is undefeated in this tournament, and team 3 is winless.
A directed multigraph can be used to model calls where each telephone number is represented by a vertex and each telephone call is represented by a directed edge. The edge representing a call starts at the telephone number from which the call was made and ends at the telephone number to which the call was made. We need directed edges since the direction in which the call was made matters. We need multiple directed edges since we want to represent each call made from a particular telephone number to a second number.
This graph is a simple graph because it contains undirected edges and has no loops or multiple edges. In a collaboration graph, vertices represent people and the edge link two people if they have jointly written in a paper.
Precedence graphs and concurrent processing
The dependence of statements on previous statements can be represented by a directed graph. Each statement is represented by a vertex, and there is an edge from one vertex to a second vertex if the statement represented by the second vertex cannot be executed before the statement represented by the first vertex has been executed. This graph is called a precedence graph.
Roadmaps depicting only one-way roads and no loop roads, and where no two roads start at the same intersection and end at the same intersection, can be modeled using simple directed graphs. Mixed graphs are needed to depict roadmaps that include both one-way and two-way roads.
The worldwide web can be modeled as a directed graph where each web page is represented by a vertex and where an edge started at the web page a and b. since new web pages are created and others removed somewhere on the web almost every second, the web graph changes on an almost.
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