A decentralized network is one without any overall dominant central hub. But instead, a network that has some nodes with a higher degree of connectivity than others, giving the overall topology local clusters with local hubs. We call this network model that has local hubs but still relatively little overall differentiation to it a decentralized network. There may be some overall center to it but it is still defined largely by what is happening on the local or regional level. To take an example of a decentralized network, we could cite the urban network of contemporary Germany. Unlike other countries such as Japan or Nigeria whose urban network is dominated by a primary node, Germany’s urban infrastructure, and the services that it provides are distributed out into a number of important centers. For example, the primary air transportation and financial hub is in Frankford, the political capital in Berlin, with Munich having the strongest economy. Each of maybe five or ten centers play a very important role in maintaining the network. There are of course many more examples we could cite, such as conglomerate corporations, political federations or distributed computer networks.
So why do we get these local level hub and spoke structures emerging? There are a number of reasons for this, but many tie back to the fact that the system is under certain environmental resource constraints, and it will only be possible for nodes to overcome some of these constraints by combining their resources. This, coupled with batch processing and the economies of scale that it enables are behind the formation of many hubs, from banks that amass financial resources to be able to fund large projects, to international airports, to the emergence of factories as local hubs in manufacturing networks. These hubs then serve the function of connecting nodes locally, but also connecting them globally to other hubs in the network. The result then is local clustering but also some global connections between clusters, and this gives us the small-world phenomena previously mentioned.
A small-world network is a type of graph in which most nodes are not neighbors of one another, but most nodes can be reached from any other by a small number of connections. A certain category of small-world network was identified by Duncan Watts and Steven Strogatz in 1998. Watts and Strogatz measured that in fact many real-world networks have a small average shortest path length, and also a clustering coefficient significantly higher than expected by random chance. This is in many ways quite counter-intuitive, as what it is saying is that even though there is a significant amount of clustering in these networks, meaning that nodes are typically highly connected to other local nodes in their cluster, and if we had quite a large network like this, then we would expect there to be quite a long shortest path length, which is not the case here. Eventually they came up with a model that captured this phenomenon. It involved starting with a ring lattice where all the nodes are only locally connected, and thus has high clustering, but then randomly picking some links to rewire so that they would likely not connect to their local cluster but somewhere else in the network. They found that you do not need to randomly rewire very many links before the shortest diameter starts dropping very quickly, and from this we are able to capture the small-world phenomena.
Six Degrees of Separation
The small-world phenomena has since gone on to be popularized in the six degrees of separation hypothesis, which is a theory that everyone is just six or fewer steps away from any other person in the world, so that a chain of “a friend of a friend” connections can be made between any two people in a maximum of six steps. Many empirical graphs are well-modeled by small-world networks. Social networks, website links on Internet, wikis such as Wikipedia, and gene networks all exhibit this small-world characteristic. We can see the small-world phenomena behind our decentralized network model, as it had these local clusters with hubs, with the hubs making global connections allowing for a relatively efficient set of overall connections to the system, without having to expend too much resources on maintaining very many global connections that are likely to be expensive and difficult to maintain.
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