#directed graph

charts showing the development of the interconnections of governmental databases

source: https://www.justice.gov/sites/default/files/jmd/legacy/2014/06/21/hear-103-1983.pdf

How Linkedin Ai-Powered Algorithms Is Built upon a Massive Knowledge Graph

What is LinkedIn’s knowledge graph?

As LinkedIn engineering team put it:

LinkedIn’s knowledge graph is a large knowledge base built upon “entities” on LinkedIn, such as members, jobs, titles, skills, companies, geographical locations, schools, etc. These entities and the relationships among them form the ontology of the professional world and are used by LinkedIn to enhance its recommender…

Graphs, Graph Representation, undirected graph, directed graph, Depth first search, Breadth first search, Spanning tree, Prim's Algorithm, Kruskal’s Algorithm, Shortest path, Dijkstra’s algorithm, Floyd’s Algorithm, Topological ordering on directed acyclic graphs, Topological ordering algorithm, Warshall’s Algorithm, Hamiltonian Paths, Applications of graphs

http://www.knowsh.com Graphs, Graph Representation, undirected graph, directed graph, Depth first search, Breadth first search, Spanning tree, Prim’s Algorithm, Kruskal’s Algorithm, Shortest path, Dijkstra’s algorithm, Floyd’s Algorithm, Topological ordering on directed acyclic graphs, Topological ordering algorithm, Warshall’s Algorithm, Hamiltonian Paths, Applications of graphs…

A partial order relation is not an object in itself. But, a set can have a partial order. We call such a set a Partially Ordered Set, or POSet for short.

So, if we make a partial order on X and call that partial order ≤, then we can just refer to the POSet as (X,≤)

We usually write sets with structure as a list*, the first being the set of elements and the rest being the bits of structure on it.

The first thing we should notice is that a POSet fulfills all the conditions to be a directed graph. This is great, since we have a convention about how to show an ordered graph. You represent each element as a circle, and each connection (a,b) by an arrow from point a to point b.

But, we can take advantage of the structure of the partial order to simplify the diagram.

Reflexivity/anti-reflexivity: We choose before-hand if we want every element to be related to itself or not. So, we add no information by including self-loops.

Transitivity: If x≤y and y≤z, then x≤z. This means that we should just show the closer pairs, and not x≤z, since it is implied.

Anti-symmetry: Since if two elements are comparable, only one comparison is true, we can take advantage of height, and make earlier things higher.

The representation that takes advantage of this structure is called a Hasse Diagram

Here are some examples: The power set, ordered by subset:

It can have multiple bottoms:

A family tree ordered by “is a descendant”:

And a linear order: