# Occurrences of nodes as the measurement duration grows

> By Matthieu Latapy, Clémence Magnien and Frédéric Ouédraogo

We conduct what we call an Internet radar measurement: from a given machine, called source, and given a set of destinations (IP addresses), we perform a traceroute-like measurement towards each of them, and then iterate this operation (6000 times here).

Each round of measurement produces an ego-centered view of the internet topology: a set of nodes and links between the source and destinations. Because of various phenomena, in particular load balancing, the observed nodes and links are not the same in consecutive rounds.

Here we compute for each node which we see during the whole measurement (identified by its IP address) the number of rounds at which it was observed and then we plot the cumulative distribution of these numbers. In other words, for each value x on the horizontal axis, we plot the number y of nodes wihch were observed during at most x rounds.

We draw this plot after 1 round, 2 rounds, 3 rounds, etc, until 6000 rounds. This gives a series of 6000 plots, which constitutes the video above.

Notice that a node cannot be observed more than the number of considered rounds, therefore the i-th plot ends at x=i.
Likewise, some nodes are not observed during the i first steps, and so the i-th plot does not in general reach y=7192, the total number of observed nodes; instead, the topmost value attained by the i-th plot is the number of nodes observed in the i first rounds. It is therefore strongly related to this plot.

We observe that many nodes are observed only a very small number of times, leading to a sharp inscrease of the plot at its beginning. Likewise, many nodes are observed almost all the time, leading to a sharp increase at the end of the plot. Notice also that there is a significant increase in the middle of the plots, which reveals that many nodes are observed in half the rounds, probably due to load-balancing.

Another interesting observation is that the initial and final sharp increases are less and less important as the measurement grows. One may then wonder if the plot converges to a steady state, and if yes to which one. To investigate this, the normalized version of this video certainly is more helpful.

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