In the last few years, a spectre has been haunting our academic and popular culture — the spectre of networks. Throughout social as well as natural sciences, more and more phenomena have come to be conceived as networks. Telecommunication networks, neural networks, social networks, epigenetic networks, ecological networks, value networks, the very fabric of our existence seems to be made of lines and points. More recently, the interest for graphs overflowed to popular culture and networks started to appear in art, graphics, advertizing, even furniture **ADD OTHER EXEMPLES**.

Our growing fascination for networks is not unjustified. Networks are powerful conceptual tools, encapsulating in a single object multiple affordances for the computation (networks as graphs), visualization (networks as maps) and manipulation of data (networks as interfaces).

In the first place and to a large extent, the success of networks is to be credited to the amazing versatility of graph mathematics. From railways to information routing, from financial to communications flows, from ecosystems to organization management graphs have found countless applications. Graph computational formalism proved so effective that we started seeing networks everywhere and transforming everything into systems of discrete but interconnected items. It would be unfair, however, to reduce networks to their mathematical properties. Graph theory has been around in mathematics since Euler’s walk on Königsberg’s bridges^{1}, but it is not until the end of the last century that networks acquired a multidisciplinary popularity. Graph computation is certainly powerful, but it is also very demanding and for many years its advantages remained the privilege of scholars with solid mathematical bases.

In the last few decades, however, networks acquired a new set of affordances and reached a larger audience, thanks to the growing availability of tools to design them. Drawn on paper or screen, networks become easier to handle and obtain properties that calculation cannot express. Far from being merely aesthetic, the graphical representation of networks has an intrinsic hermeneutic value. Networks become maps and can be read as such.

Finally, the encounter with personal computing has recently turned networks into tools for data manipulation. Not only network-like visualizations are employed in a growing number of digital interfaces, but more and more specialized software has been designed to support the exploration of network data. Tools like Pajek (vlado.fmf.uni-lj.si/pub/networks/pajek), Ucinet (www.analytictech.com/ucinet), Guess (graphexploration.cond.org) and more recently Gephi (gephi.org) have progressively smooth out the difficulties of graph mathematics, turning a complex mathematical formalism in a simple point-and-click interface^{2}.

Combining the computation power of graphs with the visual expressivity of maps and the interactivity of computer interface, networks accomplish the dream of the Exploratory Data Analysis (Tukey, 1977): a navigation through data so fluid that zooming in a single data-point and out to a landscape of a million traces are just a click away^{3}. No wonder that networks are popular!

The expansion of network from graphs to maps and interfaces has been impetuous and reached distant regions of science and society. Yet the visualization of networks has so far lacked of reflexivity and formalization. We designed and read networks as if their visual grammar was obvious, but the more we advance, the more we realize that this is not the case. We painfully lack the conceptual tools to think about the projection of graphs in the space. The very vocabulary we use has been borrowed from mathematics (e.g. cluster, structural equivalence…) and geography (e.g. centrality, bridging…) and need to be adapted to the new visual paradigm. This paper means to contribute to such reflection and propose a tentative framework for the visual analysis of networks.

Solutio problematis ad geometriam situs pertinentis, 1736.↩

A simple look at the URLs of the subsequent tools reveals the efforts deployed to make network-manipulation tools user-friendly and thereby available to a larger public↩

By offering a tool for datascape navigation, networks are also fulfilling the dream Gabriel Tarde, a forgotten father of social thinking, who imagined that the development of statistics would have one day allowed to overcome the distinction between qualitative and quantitative methods and between micro and macro sociology.↩

Before we move to the enunciation of the visual grammar of networks, however, we would like to briefly discuss the reasons that have delayed so far this type of reflection. These reasons date back to the very foundation of graph mathematics. In solving to the problem of Königsberg’s bridges, Euler performed the most classical of mathematics operations. He abstracted the formal structure of the problem from its empirical features: he took a city and turned it into a table of number (see figure 1). In doing so, Euler laid the foundation of discrete mathematics at the cost of separating the idea of network from its physical materializations. His operation has been so successful that, for the following two centuries and a half, the reflection on networks was dominated by their structural properties, with little interest for practical applications. One of the consequences of such focus on structures (at the expenses of the actual contents of networks) has been that mathematicians never saw the interest of representing networks. For them, design a network was (and still is) perfectly useless.

FIGURE 1

The idea that it could be worth to draw a network to see what it looked like came from a different tradition: the tradition of social networks analysis. Jacob Moreno, founder of this approach, was very explicit about the importance of visualization: “A process of charting has been devised by the sociometrists, the sociogram, which is more than merely a method of presentation. It is first of all a method of exploration. It makes possible the exploration of sociometric facts” (1953, pp. 95-96). Since Moreno and

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