The 80/20 Rule

– economics has a ruling system, found by Vilfredo Pareto; it has been morphed into a wide range of truisms: 80 percent of profits are produced by only 20 percent of the employees; 80 percent of customer service problems are created by only 20 percent of meeting time, and so on etc.

– power laws: a relationship between two quantities such that one is proportional to a fixed power of the other.

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Rich Get Richer

– 1: the number of nodes is fixed and remains unchanged throughout the network’s life; all nodes are equivalent

– 2: the web continues to grow incrementally node by node; this is in stark contrast to the assumption of the network models which assume the number of nodes in a network is constant over time

– 3: it is relatively easy to model a growing network; it is achieved by adding node by node; growth alone cannot explain the emergence of power laws

– 4: when deciding where to link on the web, we follow preferential attachment; when choosing between two pages, once with twice as many links as the other, about twice as many people link to the more connected page; thus, while our individual choices are highly unpredictable, as a group we follow strict patterns

– 5: real networks are governed by two laws; that is, growth and preferential attachment; each network starts from a small nucleus and expands with the addition of new nodes; then these new nodes, when deciding where to link, prefer the nodes that have more links

– 6: growth offers a clear advantage to the senior nodes, making them the richest links; preferential attachment induces a rich-get-richer phenomenon that helps the more connected nodes grab a disproportionately large number of links at the expanse of the late coming nodes; this natural leads to the power laws observed in real networks

– 7: the scale-free model demonstrates that two simple laws of growth and preferential attachment may solve the puzzle of hubs and power laws; in complex networks, a scale-free structure is not the exception but the norm, which explains its ubiquity in most real systems

– 8: by viewing networks as dynamical systems that change continuously over time, the scale-free model embodies a new modelling philosophy