Paper: “Introduction to Network Mathematics”
Title: “Introduction to Network Mathematics”
Author: Bruce Hoppe, Professor at the Boston University
Publish Date: Live online document from spring 2007
This is the first paper that purely fit in the Math’s category. Basically its content is a bunch of mathematical concepts well organisez and easy to understand by not purely math-people (like me
.
First parts of the document can be a bit boring as it takes a quite big walk around basic concepts on sets, graph’s theory, trees, … But there are some interesting things specially in the graph’s section. We are used to be explained maths as a purely theorical thing, that’s really boring. Instead, in this document you’ll find real approaches where solutions based on this theory are explained and that’s something to be thanked of.
One of my faovourite sections in this document is the one dedicated to the concept of Structural Equivalence, I do really recommend it if you’re interested in understanding the basics on social networks and recommendation systems. Also is interesting when the author explains how bipartite graphs can be really useful when working in a tags-based system.
Another important section you’ll find here is about the way the Google’s PageRank does its work. Maybe not so deeply that other document may do, but enough to understand the basics and getting conscience of the complexity it has, something that makes you think about how to face up to a highly recursively problem. It uses as an example the HopRank, a simpler PageRank concept for better understanding.
Once again, the big point you’ll find in this document is the amount of real and easy to understand examples against the minimun theory concepts necessary to understand them.

