Graph Theory

Graph Theory is ultimately the study of relationships. Given a set of nodes & connections, which can abstract anything from city layouts to computer data, graph theory provides a helpful tool to quantify & simplify the many moving parts of dynamic systems

Weighted graphs add additional information to the relationship between two nodes. This is done by assigning a numeric value to the edge  the line that connects the two nodes. This value could represent the distance or how  two nodes are connected. A real world example of a weighted graph is Google Maps.

When you look up directions for a location, Google Maps determines the fastest route, which is usually determined by finding the shortest distance between the beginning and end nodes.




An undirected graph is when each node has a reciprocal connection. So, you could say A is connected to B and B is connected to A. A real world example of this is when you add a friend on Facebook. Each user now has full access to the other user’s public content.

Undirected Graph Example — Facebook Friends

In a directed graph, the connections between two nodes is not necessarily reciprocated. So, A can connect with B but B is not automatically connected to A. A real world example of a directed graph is followers on Instagram. When you follow a new account, that new account does not automatically follow you back.

This is represented in the graph below where some arrows are bi-directional and others are single directional.



Bipartite Graph:

If the vertices of a graph can be divided into 2 such subsets that are mutually exclusive (intersection should be null set) and mutually exhaustive (union is set of all vertices) and the edges are across the 2 sets, not within the same set, then it is said to be bipartite







Complete Graph:

Have you ever considered social media to be mathematical? Believe it or not, it is! Look at it like this: we'll represent each person in a social network as a point, and if they're friends on social media with other people in the network, then we will draw a line between those two people's points. Two examples of this are shown in the images below:







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