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Mathematical Representations of Networks

A local community, a subway system, a group of friends and the internet are all networks, in some cases simple, in some cases so complex it takes a building full of computers to manage them. But what they all have in common is that they can be represented as individual entities (a person, a web-page, a train station) and their relationships (friendship, a hyperlink, a rail connection). In mathematical terms, these individual entities are called nodes or vertices (plural of vertex) and the relationships are called edges; taken together these node and edges form a graph - a superbly powerful tool for analysing the properties of any network imaginable.

Image by Campaign Creators


Graph vs Relational Databases

Graph databases (such as TigerGraph, NEO4j, etc.) are a data storage and retrieval technology with relationships at the core of their architecture and design; unlike relational databases (such as Oracle, MS SQL server, etc.) which store data as flat tables joined by keys. By natively storing nodes and relationships as core objects, graph databases are orders-of-magnitude faster at providing relationship insights in datasets, giving them a substantial competitive advantage over relational database technologies for graph data storage and analytics.


What can you analyse using graph theory?

Graph analytics is a branch of mathematics which focuses on the properties of networks. It can help answer questions like: how are customers segmented across a social network? What alternative routes would deliveries have to take if a transport link shut down? How would a change in oil price affect my landed-cost? Has a loan application been made by legitimate customer or a member of a fraud ring? And so-on. Any number of questions across any field with relationship data can benefit from the use of graph theory.

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