In the blog post, the author explores how to manage user permissions within a file system using Ruby bindings for the Neo4j graph database. The post outlines the process of setting up an example application on Ubuntu, detailing how user groups and resources, termed as 'principals' and 'content,' are managed through a graph structure. By leveraging Neo4j's ability to create relationships, the author demonstrates how to establish connections between users, groups, and content nodes, using specific relationship types such as 'PRINCIPAL' and 'IS_MEMBER_OF_GROUP.' The post further details the implementation of security relationships with boolean flags for read and write permissions, illustrating how these permissions can be checked through a traversal algorithm that assesses access rights based on proximity within the graph. The post concludes by providing resources for further exploration of Neo4j and its capabilities.