> By Frédéric Ouédraogo and Clémence Magnien

It is possible to explore the internet’s topology by tracing the paths between some *source* machines and some *destination*

machines. In this way one obtains a subset of this topology. We study here the reliability of the observed properties of this topology, i.e. whether the properties of the subset are properties of the real topology.

In this plot we show the impact of the number of sources and destinations used on the observed average distance. Each rectangle of coordinates *(x,y)* in this plot corresponds to a graph obtained with *y* sources and *x* destinations. The rectangle on the top-left corresponds to 11 sources and 3000 destinations. The color of each rectangle corresponds to the average distance of the corresponding graph. The gray variation is linear, from 0 represented by black, to the maximum observed value represented by white. The white line represents the 50% level line, i.e. all points on this line correspond to half the maximum observed value.

In this plot we observe fluctuations for small numbers of sources and destinations. For instance, with one source the graph is close to a tree, and the average distance is therefore over-estimated. It changes quickly when only one more source is considered. However, the color becomes uniform once a relatively small number of sources and destinations is attained. This shows that the observed average distance does not change much when adding more sources and destinations. The observed average distance with our 11 sources and 3000 destinations is therefore probably close to the real value.