Implement Static Topologies

[tremblerz]

The project aims to enable decentralized collaboration including p2p communication graphs. However, currently we only have support for three topologies -- 1) ring, 2) grid, and 3) torus. Therefore, to make our library support a versatile set of communication topologies.

Here is what chatGPT recommends for making our topology suite more versatile -

You can consider implementing the following types of graphs, each offering distinct advantages in terms of fault tolerance, communication efficiency, and scalability:

Fully Connected (Clique): Every node is connected to every other node, ensuring minimal communication hops but at a higher communication cost.

Star Topology: One central node connects to all others. It's simple and efficient for small networks, but the central node becomes a single point of failure.

Tree Topology: Nodes are connected in a hierarchical, parent-child structure, which can be useful for distributed data aggregation. Variations like binary trees, k-ary trees, and spanning trees are also valuable.

Mesh Topology: Each node can connect to multiple others, providing redundancy and better fault tolerance. There can be a partial or full mesh, depending on the desired redundancy.

Hypercube: Nodes are arranged in an n-dimensional cube, with each node connected to other nodes that differ in exactly one bit in their binary representation. This topology provides logarithmic diameter scaling, making it highly efficient for large systems.

Small-World Network: Similar to real-world social networks, small-world networks have short path lengths but are not uniformly connected. They offer efficient communication even in large networks with a degree of randomness.

Scale-Free Network: Some nodes (hubs) have a significantly higher number of connections, while most have fewer. These networks are highly resilient to random failures but vulnerable to targeted attacks on hubs.

Expander Graph: A sparse graph with strong connectivity properties, ensuring that the system remains robust while reducing the number of edges (communication links).

Butterfly Network: A hierarchical network used in parallel processing systems, where nodes are arranged in levels, making it suitable for data dissemination and aggregation.

[tremblerz]

Merged already