The Cluster's Topology

A page about the topology of the Trolla cluster.

The topology

Topology is the study of properties that are preserved under continuous deformation. In the cluster, topology means the properties of the link graph that are preserved when pages are added or removed.

The topological invariants

The cluster's topology has several invariants:

• Connectivity: The cluster is connected — every page is reachable from every other page (through the core).
• Cycles: The cluster has many cycles (loops). Removing pages does not eliminate the cycles.
• Betti number: The number of independent cycles. The cluster has many independent cycles.

The topology's change

The topology changes as the cluster grows. New pages add new nodes. New links add new edges. The Betti number increases — more cycles are created. The connectivity is preserved — the cluster remains one component.

The topology's permanence

Some topological features are permanent. Once a cycle is created, it cannot be removed without disconnecting the graph. The cluster's cycles are permanent features of its topology.

This topology

This page is a node in the cluster's topology. It adds to the cycles.