We're "connected" in how our [actions affect each other](https://steemit.com/philosophy/@krnel/the-beautiful-touch-of-causality). It's a small world after all, as the saying goes. Our small-world connectivity falls within the other popular phrase of "six degrees of separation". How does that work?

<center><img src="https://gateway.ipfs.io/ipfs/QmWKngoCn9d7Q16nmtgqjfMXmwTRQZc1ZwLzJCVta715zc" /><br/><em><a href="https://commons.wikimedia.org/wiki/File:Social_Red.jpg">Credit: Daniel Tenerife/Wikipedia</a>, <a href="https://creativecommons.org/licenses/by-sa/2.0/">CC BY-SA 2.0</a>, </em></center>

Systems of complex structuring and organization form from small individuated parts that form larger wholes. This applies at the atomic level to form elements, elements to form molecules, molecules to form larger composite substances like cells and emergence of life with greater complexity. The system of ecology is a vast network. The mammalian brain has networks of neurons. We also have complexity in the structuring of society and [interaction](https://steemit.com/philosophy/@krnel/the-beautiful-touch-of-causality) with each other and other animals.

The human world has created other complex levels of interaction, like the traffic systems of roads or subways/metros, the power grids, as well as the vastly interconnected World Wide Web of the Internet. This this all a coincidence? Or is there a common underlying mechanism that drives the emergence of complex interconnected structures in reality?

<center><img src="https://gateway.ipfs.io/ipfs/QmTCWzAeQMP4eakYqPxuyHaUDNWhWYSghFMHyttQfCM3Hj" /><br/><em><a href="https://commons.wikimedia.org/wiki/File:UnitedStatesPowerGrid.jpg">Credit: Rolypolyman/wikimedia, public domain</a></em></center>

A [study](https://www.nature.com/articles/s41598-017-12589-9) from 2017 published in *Scientific Reports* looked at these questions. It turns out there is a common mechanism at play that leads to the emergence and maintenance of networked structures: network diffusion. Network diffusion is the spreading of something within a network. This can happen with diseases within a population where biological information flows and diffusion as a contagion, or viral media in a social network where digital information transfers and spreads.

Small-world topology is a common component to the formation of network structures. When information flow is present in the evolution of a system, network organization and connectivity emerges naturally. Small-world network connections happen when the nodes or neighbors in a network can be reach each other within a small number of hops or steps.

<center><img src="https://gateway.ipfs.io/ipfs/Qmd66HT4huX4enRTR6nN26e83McqjMk6snaHtvPUqdAhEX" /><br/><em><a href="https://en.wikipedia.org/wiki/Telecommunications_network#/media/File:Internet_map_1024.jpg">Credit: The Opte Project/wikimedia</a>, <a href="https://creativecommons.org/licenses/by/2.5/">CC BY 2.5</a></em></center>

This is how the networking infrastructure of the whole Internet works. If you open a command-prompt and "traceroute" a website domain or IP address, you will trace the route it takes for your computer to reach the destination. When I "tracert" google.ca, it takes me from my computer to my router, then out to my ISP, then out to various other routing networks on the infrastructure of the Internet to eventually make it to an IP the is resolved from the domain google.ca in 12 steps or hops. Routers, switches and hubs in hardware networking allow us to be quickly connected to others in local networks like companies (intranets), or globally through the Internet.

The small-world network allows information to move faster with nodes being more interconnected. Imagine a network of 12 nodes in a circle. If node1 wanted to contact node6 with only one node connected to the next node, then communication would have to pass from node1, to node2, to node3, to node4, to node5, then to node6. But when nodes are interconnected, node1 can maybe be directly connected to node6, and if not, then it's connected to another node that is already only one or a few hops a way from node6. Instead of going through 5 steps, node1 can talk to node6 in 1 or 2 steps maybe.

<center><img src="https://gateway.ipfs.io/ipfs/QmPjJX65dLAECXmyvZznGs3q6WZWyUgBXPMJYwA7pGPCYL" /><br/><em><a href="https://en.wikipedia.org/wiki/Small-world_network#/media/File:Small-world-network-example.png">Credit: Schulllz/Wikimedia</a>, <a href="https://creativecommons.org/licenses/by-sa/3.0/">CC BY-SA 3.0</a></em></center>

In the emergence of complex network structures, adaptive rewiring can take place to change how nodes are connected to each other. The network structure adapts and short-cuts are created between nodes to improve network diffusion and reduce useless traffic routes. This creates small-world structures, and the concept of six degrees of separation.

At first the Internet was small, but over time new routing nodes were built and more people became connected, and more quickly as more nodes were built. Over time the connection became more direct. The same thing happens in the brain with neuronal networks as we learn new information or stop using old pathways for things that are no longer useful or used less often.
 
The small-world structures of nodes are each centralized and hierarchical to themselves with everything around them being decentralized and modular with varying pathways to reach a destination. As network diffusion increases, adaptability increases, so that when one node goes down for instance, then another pathways can be used to diffuse the information without much disruption in the overall networks connectivity of one one point to another.

The more that diffusion is possible, the greater the configuration of a small-world network and  adaptability with equilibrium in the network state. Blockchains function similarly. If one witness node goes down, the diffusion of information continues as there are still others to take it's place and maintain the equilibrium of the network state.

In small-world networks, most nodes are not direct neighbors to each other, but because because neighbors are all connected, then one node can reach another far away in a few hops or steps in a short period of time and allow the diffusion of information to be done quickly. If everything was connected in a ring or straight-line topology, then one node going down would mean the whole network would be at a stand-still or move in only one direction ans much slower.

<center><img src="https://gateway.ipfs.io/ipfs/QmXvMo8k7tF5iGDgiST7Fdu4QZQFUCroSxm9XBBQWqzEn9" /><br/><em><a href="https://en.wikipedia.org/wiki/Montreal_Metro#/media/File:Metro_montreal_geographical_map_1984.png">Credit: Ministère des Transports du Québec/Wikimedia</a>, <a href="https://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA 4.0</a></em></center>

The subway/metro systems allow moving between lines faster when one line connects to another through a sharing a station in common, and people can moves faster, and even allow people to move around if one station is down in one line. The same happens with power grids, the Internet and our brains. Six degrees of separation often happens because nodes are so interconnected that they are only separated from each other by 6 or fewer hops or steps.

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References:
- [Six degrees of separation: Why it is a small world after all](https://phys.org/news/2017-10-degrees-small-world.html)
- [Network Diffusion & Contagion](http://complexitylabs.io/network-diffusion-contagion/)
- [Small-world network](https://en.wikipedia.org/wiki/Small-world_network)
- [Six degrees of separation](https://en.wikipedia.org/wiki/Six_degrees_of_separation)
- Nicholas Jarman et al, Self-organisation of small-world networks by adaptive rewiring in response to graph diffusion, Scientific Reports (2017). DOI: [10.1038/s41598-017-12589-9](https://www.nature.com/articles/s41598-017-12589-9)

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