deletions | additions       diff --git a/network regions.tex b/network regions.tex  index 40edc08..7b3359f 100644  --- a/network regions.tex  +++ b/network regions.tex 
...
\section{Step 1: Network \section{Network  regions} \subsection{Reading principle} 
...
This translation is not free from distortions. Some properties are clearly visible, others are not. Some of the things that can be observed are meaningful, other are not. For example, the absolute position of nodes and cluster (at the top or bottom, left or right of the image) is completely arbitrary. What counts is the relative position of the nodes, their agglomeration and their separation. What matters is the clustering of the network.  To be sure, clusters could be detected in other ways. Andrea Noak, in particular, has shown that the mathematically mechanism of force-vectors correspond to the computation of the clusters by modularity , ,  a technique often used to detect communities in networks . .  Mathematical clustering however imposes a dissection of the network that is often too clear-cut. The advantage of visual techniques discussed in this article is that their fuzziness allows negotiating the frontiers of the clusters. These frontiers are naturally blurred, since clusters are not exclusive categories, but shades of density. Clusters may have clear boundaries, like cliffs separating a plateau from the valley, but most of the time their borders are gradual as the slopes of a mountain. The fuzziness of clusters’ frontiers, by the way, is no obstacle to their recognition: a mountain is easy to see even is it impossible to say exactly where it starts and ends. What is important is to be able to distinguish the clusters and to identify the empty zones between them. These zones are called “structural holes”. The larger these holes are, the more they denote the absence of connection between the clusters. Such absence is often the symptom of an opposition. Finally, we can remark that often the biggest clusters are themselves composed by smaller (and less distinct) sub-clusters. Large structural holes can be read as strong oppositions, while smaller holes denote distinctions without opposition.