Tag Archives: power law

Networks; The Power of Hubs

How do some  webpages on the Internet become so ubiquitous that we are rarely ever less than two short links away from viewing that page? How have some webpages become so popular among the hundreds of billions of webpages that are on the Internet currently, not to mention the new ones that pop up almost every second? More importantly how do certain pages become the centre for web activity and lead us to other pages within their network? Albert-Lázló Barabási explored these questions about networks and the organization/disorganization of interconnectivity within his Chapter titled Hubs and Connectors .

Barabási begins the piece by explaining both the power and importance of links within the web. Quite simply the larger number of Continue reading

He has Connections… How can I get to know Him!!? Network.

The reading for this week, Linked by Albert-Laszlo Barabasi disproves the idea of randomness in networks and champions the idea of hubs and connectors that function to bring together society. The idea behind linked and being connected to others is not new nor is it phenomenal: it is in our blood. This is our history and thus, inevitable. The Bible clears demonstrates this connection as in the beginning, there was Adam, then Eve, then Cain and Able. After that, humanity arises and creates towns to settle and we develop. Thus, we are all connected or linked in some way. If one is agnostic or believes in science, then think of evolution. People evolved as running from animals to hunting them in groups. Once in groups, they became nomads, and then quite surely, someone decided to settle down in a location, therefore forming a town. Thus a hub is created and with it, streets, other towns, etc…

It is divided into 3 chapters. I will discuss each chapter separately by its part and tie it together at the end. They are all connected; rather, they are components of a larger truth.

The Fifth Link: Malcolm Gladwell’s The Tipping Point notices an interesting phenomenon: “sprinkled among every walk of life…are a handful of people with a truly extraordinary knack of making friends and acquaintances. They are connectors” (55). This brings in the idea of connectors as highly relevant components of our social lives. Another way to define connectors is by calling them hubs. These hubs have a large number of links. One can create the analogy of a large city, such as Los Angeles and the suburbs that surrounds it. Many highways enter and go out of Los Angeles, connecting many different cities along the way. This discovery has basically disproven Erdos-Renyi’s theory of random worldview and Watts and Strogatz’s simple circle network model. Social networks exhibit clusters and hubs, both points that demonstrate a worldly rule that applies.

We can also apply the theory of links and connectors/hubs to cyberspace. The World Wide Web is the ultimate space for freedom, an environment that represents and defines the meaning of space without limits, boundaries, nor rules. Anyone can publish their work online and allow anyone to see it. Problem is, there are billions of websites. The question that arises is visibility. On the Web, the “measure of visibility is the number of links. The more incoming links pointing to your Webpage, the more visible it is” (57). As such, only websites that become hubs are highly visible (Amazon, Google). These are hubs: connectors with enormous links to other nodes.

I can create a website, thus it becomes a node. Google has grown, thus it has become a hub. Without a link, both websites exist and move in different worlds, or just space. The internet is as big as the universe, each node moves on its own, until it makes contact. This is the link. My website can function in its own galaxy as networks tend to form a cluster. Clusters are “nodes that are linked only to nodes in their subculture or genre” (61).  As a cluster, it is easier to find a common connection to a hub. For example, if my website is about knee pains, then I would like to create some link to a popular website such as WebMD. This in turn, can allow me to link with Google. In two links, my website has escaped randomness and can be visible.

The Sixth Link: Vilfredo Pareto may be a well known Italian economist, but I feel that his thought process behind the 80/20 Rule is sheer brilliance. It is all around us, and yet, he is the first to notice that it applies to the world. This is Simple Genius: understanding a law within the world that is so visible, and yet, invisible to the eye. 80/20 Rule applies to many things, but is generally regarded as 20 own rest of the 80. This also applies to network as well. It can be proven through a mathematical expression called a power law. In contrast to a bell curve, which is a “distribution rather similar to the peaked distribution characterizing random networks,” (67) the power law is by definition a special kind of mathematical relationship between two quantities. The exact definition is as follows: if one quantity is the frequency of an event, the other is the size of the event, then the relationship has a power law distribution when the frequency of the event decreases at a greater rate than the size increases. In layman terms, think of 20% of the population ruling 80% of the world.

Power laws basically functions to prove mathematically the fact that in most “real networks the majority of nodes have only a few links and that these numerous tiny nodes coexist with a few big hubs, nodes with an anomalously high number of links” (70). Again, this relates to Gladwell’s idea of connectors, but proving quantitatively that it exists within the realm of the World Wide Web. It demonstrates that real networks are not random at all, but exist under the power law. The interesting idea that Barabasi proposes is that in the beginning, nodes tend to be chaotic and without any form or order. However, through time, this disorder turned into order through self-organization. Under the theory of phase transitions, real networks demonstrate self creation from disorder into the 80/20 Rule. Barabasi’s idea is highly compelling, as he demonstrates quantitative analysis and by using the Web, a blank space which is like a universe unto itself, to explain a simple law that applies to the world. Everyone is intricately linked, because we are social beings. Networking is only a function of humanity, which always existed, but has now been proven through the power law. A question that arises is why do hubs and links form and how does it form in such a manner that to the naked eye is so random and chaotic, and yet, has order.

The Seventh Link: Erdos and Renyi’s model of networks rely on two principles. First is the idea that all nodes are fixed and remains unchanged throughout the network’s life. Second is that all nodes are equivalent. However, this is obviously not the case as there exists hubs/connectors, links, and change from disorder to order through self-organization. To understand how it does this, we must understand that the web is constantly growing. It is changing and growing. This is quite self-explanatory. There has been exponential growth of websites on the World Wide Web. As there is growth, we can safely disprove the static nature of Erdos-Renyi’s model of networks. We also do not randomly decide on which websites to link. We choose based upon our knowledge and social upbringing. We prefer certain websites over others because we are comfortable and familiar with that certain product. Thus, rises the concept of hubs. Barabasi brings up the idea of preferential attachment: “when choosing between two pages, one with twice as many links as the other, about twice as many people link to the more connected page. While our individual choices are highly unpredictable, as a group we follow strict patterns” (85). In many sense, this is true. We are all sheep and follow the leader.

In truth, randomness does not really exist unless it is the role of a die. Linking between networks is not random. Though unmentioned as third criteria, I believe that popularity and attractiveness plays an important role in the addition of links and creation of hubs. Webpages that have more links are more likely to be “linked to again” (86). Thus, there exists first person advantage. Older nodes have greater chances to become bigger and eventually rise as a hub. As a senior member within a link, this node has greater links and more nodes want to be linked to that certain node. Barabasi has given compelling evidence that real networks are not random, but constantly evolving and growing, attracting more links through the legitimacy of the power law.

We are living in a complex world and yet, guided by the invisible hand or law that is, in my opinion, inexplicable. The idea of real networks applies not only to websites, but to humanity in large. I believe that Barabasi’s point is that humans are social beings and we are followers. There are different people: some are leaders and some are followers. This difference guides the principle of 80/20 Rule as well as the power law. Barabasi has done something quite remarkable: take a simple, obvious, and yet invisible rule, and proved it scientifically and gave it a name. Kudos.