# The Topology of Onlife Networks

Several spontaneous orders on the internet present the topological features of scale free-networks and “small worlds.” To grasp how the complexity of such topological properties affect any political planning, have a look at Fig. 3 with the key parameters of every network, namely (i) its nodes, (ii) the average distance between nodes or diameter of the network, and (iii) its clustering coefficients. This allows us to single out three models.

The first one is represented by a regular network in which all of the nodes have the same number of links: this network has high clustering coefficients but a long diameter since the degree of separation between nodes is high.

The second model is a random network with opposite features: it presents low clustering coefficients but a very short diameter. The explanation is that random links exponentially reduce the degree of separation between nodes in the network.

The third model is a small world-network: its peculiarity depends on the apparent deviation from the properties of both regular and random networks. Like regular networks, small world-networks present high clustering coefficients, but they also share with random networks a short characteristic path length, *i.e.*, the nodes of the network need few steps in order to reach each other.

As you can see, in light of Fig. 3, in the regular network there are 20 nodes, each of which has 4 links, so that the blue node (the brighter one on the left) would need at least 5 steps to reach the red one (the brighter on the right). What is striking with a small-world network is how random links exponentially reduce the degree of separation between nodes: for instance, if 3 nodes are randomly rewired, the degrees of separation decrease from 5 to 3. This means that, in a circle of 6 billion (people) nodes as our world could be represented today, if random links in the network would be about 2 out of 10,000, the degree of separation turns out to be 8. But if they are 3 out of 10,000, then 5!

Since the pioneering work of Stanley Milgram (1967) and, later, of Mark Granovetter (1973), the idea of small world-networks became in few years one of the key words of contemporary scientific research by fostering a large set of empirical studies on the topology of complex systems. Significant effort has been made in order to structure analytical models able to capture the nature of small worldnetworks. Here, it suffices to mention only two of these. The first small worldmodel was proposed by Duncan Watts and Steven Strogatz (1998): they suggested to randomly rewire a small fraction of the edges belonging to a low-dimensional regular lattice so as to prove that the degrees of separation in the network would exponentially decrease. Yet, contrary to random networks, the shortening of the diameter proceeded along with high clustering coefficients as in regular networks. These small world-features explain the results of Milgram's and Granovetter's research because short diameters of the network and high clustering coefficients quantify both the low degrees of separation between two citizens picked up randomly in such a complex network like the American society studied by Milgram in the mid 1960s, and the “strength of weak ties” stressed by Granovetter in the early 1970s.

The second analytical model we need to examine was defined by Albert-Lászlo Barabási (2002): he noted that most real world networks, such as the internet, grow by continuous addition of new nodes whereas the likelihood of connecting to a node would depend upon its degree of connectivity. This sort of special attachment in a growing system explains what Watts and Strogatz apparently missed, namely, the power-law distribution of the network in a topological scale-free perspective: small world-networks in the real world are indeed characterized by few nodes with very high values and by most nodes with low connectivity. The presence of hubs or of a small fraction of nodes with a much higher degree than the average offers the key to comprehend why small world-networks can be both highly clustered and scalefree. This occurs when small, tightly interlinked clusters of nodes are connected into larger, less cohesive groups.

Drawing on this research, we can deepen the notion of complexity mentioned in the introduction. Today's onlife *kosmos* can indeed be comprehended in accordance with the nature of the hubs and the degree of their connectivity in a small world network, because the emergence of spontaneous orders, *e.g.* peer-to-peer (P2P) file-sharing systems on the internet, often goes hand in hand with the hierarchical structure of these networks (Pagallo and Durante 2009; Glorioso et al. 2010). Significantly, in *The Sciences of the Artificial* (new ed. 1996), Herbert Simon insisted on this point, *i.e.*, the notion of “hierarchy” as the clue for grasping the architecture of complexity and, moreover, the idea of “nearly decomposable systems” that reconciles rigid top-down and bottom-up approaches. In the wording of Simon, “the clusters of dense interaction in the chart” of social interaction “will identify a rather well-defined hierarchic structure” ( *op. cit.*, p. 186). Furthermore, according

to the “empty world hypothesis,” the term of near decomposability denotes that “most things are only weakly connected with most other things; for a tolerable description of reality only a tiny fraction of all possible interactions needs to be taken into account” (Simon 1996, p. 209). Recall the difference between regular networks, random networks, and small worlds, mentioned above: Simon's “empty world hypothesis” corresponds to the notion of hubs, since such hubs not only offer the common connections mediating the short path lengths between the nodes of the network, but also elucidate the clusters of dense interaction and complexity in the chart of social relationships.

These topological properties of the network introduce a crucial point on how the structure of the *kosmos* may affect the political planning of the *taxis* and, hence, any “good onlife governance.” Whilst I assume that there is no *kosmos* without *taxis* in the “onlife experience,” governance actors should really know the subject matter which they intend to govern. The point can be illustrated with the words of Paul Ormerod:

In a scale-free network, we know that we need to identify the well-connected individuals and to try by some means to induce them to change their behaviours. In a random network, we know that there is a critical value of the proportion of agents we need to influence in order to encourage or mitigate the spread of a particular mode of behaviour or opinion across the network. This at least gives us an idea of the scale of the effort required, and tells us that money and time which is unlikely to generate the critical mass is money and time wasted. In a small-world context, targeting our efforts is more difficult, but at least we know that it is the long-range connectors, the agents with links across different parts of the network, or who have connections into several relevant networks, who are the most fruitful to target. (Ormerod 2012, p. 275)

Yet, a crucial aspect of the analysis concerns more the evaluation, than the description, of the *kosmos*, which *taxis* aims to discipline. Lawmakers, policy makers and governance actors should not only know whether they are dealing with a random network, a small-world network, a scale-free network, and so forth, since they have to evaluate the kind of information that is distributed according to the topological properties of a regular network, a random network, etc. Consider the following spectrum in the field of social interaction, which empirical evidence has proved to be a small world network: at one end, the “small worlds” of the internet in the early 2000s and their positive effects (Barabási 2002); at the other end, what the COPLINK program illustrated in the mid 2000s, namely that “narcotics networks are small-world with short average path lengths ranging from 4.5–8.5 and have scale-free degree distributions with power law exponents of 0.85–1.3” (Kaza et al. 2005). In between, we find more controversial cases, such as the “small worlds” of some P2P networks as Gnutella (Pagallo and Ruffo 2007). In light of this spectrum, let me reassess the different levels of analysis illustrated above with Fig. 2. From an ethical viewpoint, what should be avoided or minimized is the “impoverishment of the infosphere,” or entropy, whilst “the flourishing of informational entities as well as the whole infosphere ought to be promoted by preserving, cultivating and enriching their properties” (Floridi 2006). From a legal and political stance, what is at stake here concerns the ways in which the new scenarios of the information revolution have suggested national and international lawmakers more sophisticated

**Fig. 4 How game designers may shape the onlife experience**

forms of legal enforcement, complementing the traditional hard tools of the law, much as softer forms of legalized governance, such as the standardization of best practices and guidelines, through the mechanisms of design, codes, and IT architectures. Many impasses of today's legal and political systems can indeed be tackled, by embedding normative constraints and constitutional safeguards into ICTs. After the topological properties and ethical challenges of the current *kosmos*, let me examine this *taxis*-side of the onlife governance separately: the next section explores how game designers may shape the onlife experience.