As a student of statistics and business, I have always enjoyed learning and applying probability distributions in different settings. I have been interested in complex systems and the role of chaos and fractals for quite some time, and recently started reading physicist Albert-László Barabási’s book on network science called Linked, published in 2002. I spend a large part of my day job thinking about the stock market, the financial services industry, and blockchains, all of which share features of complex systems such as fractality and adaptivity. I couldn’t help but start thinking about network topologies along the discourse of Web3. Is the rise of centralized platforms in the topology of Web 2.0 an inevitable effect of a complex system self-organizing? If the Internet and the Web, as well as most complex networks in nature and human history, have self-organized around power laws when left to their own devices, would the topology of Web3 also become scale-free and consequentially dominated by a few hubs? My thoughts are fluid and the writing below is not intended to answer these questions; most importantly, I wanted to open up a discussion forum and have a chance to benefit from the research and perspective of those more educated on the topics.
From cellular metabolic networks to terrorist webs, most networks in the real world are dominated by hubs – a minority of nodes with an extraordinarily large number of links. The distribution of links in most real networks do not follow the normal distribution contemplated by Erdős and Rényi in their random graph model but a power law distribution. Whether it’s the Internet, the dissemination of infectious diseases, or the global economy – most real networks are “scale-free” and exhibit growth and preferential attachment. Networks grow by adding one node at a time, and new nodes are more likely to attach to nodes with a high number of existing connections. Networks formed following such premises end up with a minority of highly connected nodes, or hubs, and are scale-free. They are called scale-free because the distribution of links on such networks follow power laws, which do not have any characteristic scale; hence there is no average node in such networks. There are other nuances to networks in real life, although the scale-free model offers a solid starting point. For instance, nodes are not homogenous, and some are inherently more competitive than others in terms of grabbing links. While Google was not one of the first popular search engines created, it became the biggest node through its superior algorithm.
Paul Baran, a pioneer of the Internet and inventor of packet switching, was thinking about the optimal structure for the Internet in the 1960s before the APRANET took shape. He believed that a distributed, mesh-like network with sufficient redundancy is the most resilient structure. Colloquially, many of us use the “Internet” and the “Web” interchangeably. However, the Internet is really a network of routers communicating with each other through protocols, while the Web signifies the network of information that we access via the Internet. The Internet as we know it today was not centrally designed, partially because Baran’s vision of distributed networks was ahead of his times; in contrast, the Internet emerged one node at a time. The Internet is open in the sense that anyone can add nodes and links to it without permission, and as a result has evolved and taken a shape of its own. In 1999, researchers found that the distribution of connections among routers on the Internet follows power law. Barabási and his research team has found that as the Internet grows (i.e., more routers, or nodes, are added), routers with more existing links tend to gain more links than nodes with fewer links. At around the same time, parallel discovery was made that the topology of the Web had evolved to follow the power law. As Barabási neatly explained, the Web’s architecture is a function of the code (i.e., the software) and users’ collective actions, and the architecture controls everything from formation of Web communities to discoverability of Webpages. In the absence of ads, the search engines are more likely to index a Webpage with more incoming links, and the Web has a strong tendency to self-organize into a topology dominated by a minority of nodes.
The Web3 canon emerged in the face of the rhetoric that a small number of centralized platforms exerts too much power on the existing network. Google and Facebook have large, centralized Web servers containing our data, and wield great power in directing users’ collective actions on the Web. The Web as we know it today is powered by 3 protocols – HTTP, TCP, and IP. The HTTP is an application-level protocol that connects Web browsers to Web servers – when you type in a search on Google, an HTTP request is sent from the browser to the server via TCP/IP. Blockchain protocols are counterparts to HTTP and are built on top of TCP/IP. The current version of the Internet is built on a client-server architecture, which means most of our information is stored on servers, some of which are highly centralized such as those run by Google and Facebook, and users send HTTP requests to these servers. Blockchain-based networks are peer-to-peer networks, which means each node acts as both a client and a server. However, blockchain-based networks are already coalescing around a minority of nodes, and platforms such as OpenSea, Infura, Alchemy have emerged as the hubs in Web3. As Moxie Marlinspike rightfully pointed out, nobody wants to run their own server and you can’t easily run a server on your phone or in a desktop browser. As a result, a minority of nodes such as Infura and Alchemy have emerged that provide access to centralized servers as well as other developer tools. Zooming in more, we see large nodes, or “whales”, emerging on certain protocols, and VCs and early backers have come under criticism of exerting too much control over the networks. The phenomenon of “wealth begetting wealth” is certainly scalable.
The question has thus become whether Web3 networks will inevitably trend towards scale-free, with a few nodes such as OpenSea and Coinbase becoming the new hubs and centralized gateways to the underlying Web3 protocols, commanding similar positions as Google and Facebook in Web2. Does the prevalence of scale-free networks in most natural and human systems forebode the centralization of Web3? One reason that scale-free networks are prevalent is the topological robustness of such networks – researchers have found that because natural failures (different from concerted attacks) affect big and small nodes with equal probabilities, while random networks tend to fall apart after a critical number of nodes are removed, most scale-free networks such as those prevalent in our life do not have such critical threshold. In the context of Web3, centralized platforms also benefit from the ability to iterate new functionality faster (as pointed out by Moxie Marlinspike), mental availability of consumers, etc.
In physics, power laws emerge when systems are pressured to undergo a phase transition. When water freezes or metals become magnetic, the matter approaches a critical threshold, at which point all quantities of interest (i.e., the correlation length of atoms) start to follow power law distribution. Researchers of complex systems view such self-organization around power laws as a signature of the systems adapting to the edge of chaos, which describes the space between disorder to order. As complex networks are formed in real life, power laws appear to have served as the guiding principle for self-organization at each stage. The rise of large hubs is simply one of the properties of such networks. Web3 networks appear to be trending towards this direction as well – will they escape the law of complex systems?