On Network Growth
By: The BitLog Team | Last update: Aug. 2025 | 5 min read
In previous articles we suggested that bitcoin price follows powerlaw behavior in time and that this behavior is driven by the fact that it's a network whose userbase itself grows as a powerlaw.
As discussed before, powerlaw behavior is surprising for a financial asset.
Therefore, as additional support for the claims above, we show in this article that there is precedent for powerlaw growth in other networks. We also use the example of pandemics to better understand the origin of this behavior. We will learn that it tells us something about human behavior in general.
Other Examples of Powerlaw Growth in Time
Below is the growth of the internet between 1987 and 2006, exhibiting convincing powerlaw growth. The number of users and the number of hosts (computers connected to the internet) grows like time to the 6th power, i.e.
Data is shown in solid lines, and the powerlaw trendline is dashed.
Below is another example, the growth of twitter/X (2007-2013).
The number of tweets/posts again grows like time to the 6th power.
The number of users, seems to grow to the 3rd power, though data is limited.
Understanding The Spread in Pandemics
To better understand why a network might grow like a powerlaw in time, we examine the growth of pandemics, as was also suggested by @giovanni. Unfortunately this topic is a bit intense, but it can help us gain useful insight, as we will see below.
Pandemic growth is often exponential in time, as was the case for Covid-19. As an example, we plot below the cumulative number of cases in the US as a function of time during the beginning of the pandemic. Similar exponential growth was found in multiple countries and counties. (If you're not sure how to recognize exponential growth, please see our "Why Logarithmic Scale" article.)
We now compare this trend to the growth of the HIV/AIDS pandemic.
As we will see, the behavior is completely different due to the mechanism of spread. Unlike Covid, HIV spreads through intimate contact and is therefore selective among the population.
Below is a histogram showing the results of a survey of sexual activity from a 1993 paper. The somewhat surprising result is that the high-risk end of the population is distributed like a powerlaw, roughly according to the equation
where Count is the number of individuals, Rate is the rate of sexual encounters per unit time, and A is a constant. Note that this is not the same powerlaw in time we saw before, but rather a powerlaw distribution in the population.
In the chart below:
Blue solid line - histogram of results from the population survey of sexual activity.
Blue dashed line - trendline according to the powerlaw equation above, with a flat cutoff on the low risk side.
Animated color progression - a model of the spread of the pandemic through the population (see text below).
As shown in the animation above, infections spread from high risk groups to lower risk groups, infecting a large fraction of individuals in each group before moving on to the next.
The authors of the paper showed how a powerlaw distribution in the population can lead to powerlaw growth of the pandemic in time, and even predicted the correct powerlaw coefficient (i.e. time3).
The resulting growth of the cumulative AIDS cases in the US, exhibiting clear powerlaw behavior, is shown below.
To summarize, pandemics often intuitively grow exponentially in time.
In other cases, notably in HIV/AIDS, the pandemic grows like a powerlaw, likely due to a pre-existing powerlaw distribution in the behavior of the population.
To our knowledge, the AIDS pandemic is the only case where powerlaw growth in time was shown to be connected to a measured powerlaw distibution in the population, which is why we chose to include it here.
Returning to Networks
By analogy to the above, we may be able to better understand the powerlaw growth of modern networks, such as twitter/X, the internet, or bitcoin.
Presumably, there is some unknown metric (e.g. tech savviness or the willingness for network adoption or for taking financial risk) whose edge distribution in the population follows a powerlaw.
Such a distribution, if it exists, would then naturally lead to powerlaw growth in time.
We provide below an example of a possible distribution (in blue), including a progression in time of network adoption across the population, from orange, to teal, to pink.