Social networks

Albert Diaz-Guilera

We have also the statistical properties of different social networks. The examples are:

1. The Web of trust: we investigate the creation of social capital in the “web of trust” formed by the users of the “Pretty-Good-Privacy” (PGP) encryption system. The PGP program is used in digital communications both to encrypt messages—so that only the desired recipient can read it—and to authenticate documents—so that the recipient knows for sure who the author is. In the PGP web of trust, a user A certifies user B’s identity by “signing” B’s public encryption key. Signing someone else’s key is equivalent to certifying that the signee is who he claims to be, and therefore is an objective proof of trust. The web of trust—that is, the network whose nodes are the public keys and whose links are the signatures, i.e., the relations of trust—enables users to interchange private communications in a trusted way with other users who they might have not yet met. Hence, we suggest that the PGP web of trust is a social network for which one can measure the structure of the network and the formation of social capital.

1. The email network at University Rovira i Virgili: we have analyzed the email network regarding each email address as a node and linking two nodes if there is an email communication between them. To consider only the email that concerns the flow of valuable information in the organization we have eliminated emails that are sent to more than 50 different recipients and have disregarded links that are unidirectional. Surprisingly, we have found that the cumulative degree distribution is exponential. We have also focused on determining the community structure of the email network, that can be very useful in providing information on the informal chart behind the formal one. Our results reveal the emergence of self-similar properties that suggest that some universal mechanism could be the underlying driving force in the formation and evolution of informal networks in organizations, as happens in other self-organized complex systems.

1. The collaboration network at Spanish conferences on statistical physics (FISES): This colaboration network is constructed by assigning to each node a researcher in the community and linking them if they have at least coauthored a contribution during the conferences that each year and a half are held at different places in Spain. To get the detailed information, follow the link (in Spanish).

Social networks as those we have analized have several properties in common: a high clustering coefficient, positive degree correlations, and the existence of well defined communities. In order to explain the wide appearance of these characteristics we have also proposed a model where the attachment between nodes is based on the distance in a social space.

Collaborations:

1. L.A.N. Amaral, Northwestern University

2. A. Arenas, Universitat Rovira i Virgili

3. M. Boguñà, Universitat de Barcelona

4. X. Guardiola, SIMPPLE

5. R. Guimerà, Northwestern University

6. R. Pastor-Satorras, Universitat Politècnica de Catalunya