The Role of Metanetworks in Network Evolution

Abstract

The question of what structures of relations between actors emerge in the evolution of social networks is of fundamental sociological interest. The present research proposes that processes of network evolution can be usefully conceptualized in terms of a network of networks, or “metanetwork,” wherein networks that are one link manipulation away from one another are connected. Moreover, the geography of metanetworks has real effects on the course of network evolution. Specifically, both equilibrium and non-equilibrium networks located in more desirable regions of the metanetwork are found to be more probable. These effects of metanetwork geography are illustrated by two dynamic network models: one in which actors pursue access to unique information through “structural holes,” and the other in which actors pursue access to valid information by minimizing path length. Finally, I discuss future directions for modeling network dynamics in terms of metanetworks.

Keywords:

• mathematical sociology
• metanetworks
• network dynamics
• network evolution
• social network analysis
• social structure

The author would like to thank Ko Kuwabara, Michael W. Macy, Brent Simpson, and Arnout van de Rijt for comments and contributions to earlier versions of this paper.

Notes

¹Note that this not the first model of network dynamics to view network evolution in terms of a Markov process. For example, Jackson and Watts (2002) develop and implement a similar model, though the focus of their analysis is different than the present focus on the properties of metanetworks.

²A wide variety of research on network dynamics exists across the social sciences. This research concerns the dynamics of a diversity of network models including models of structural balance (Cartwright and Harary, 1956; Macy, Kitts, and Flache, 2003), group formation (Carley, 1991), social exchange (Leik, 1992; Willer and Willer, 2000; Bonacich, 2003), policy-making (Stokman and Zeggelink, 1996), status hierarchies (Gould, 2002), technological innovation (Podolny and Stuart, 1995; Stuart, 1998), and scientific collaboration (Moody, 2004).

³Some exceptions to these modeling assumptions include Bala and Goyal (2000) where actors can change all links at once, the simultaneous network formation of the so-called “Myerson game” (Myerson, 1991), Dutta, Ghosal, and Ray (2005) who consider far-sighted actors, and Leik (1992) who considers a “manipulator” proposing links that do not involve himself.

⁴A reader might suspect that the different number of isomorphs for the Box and 3-Branch might be the driving factor making the Box more probable. However, the Box actually has fewer isomorphs (3) than the 3-Branch (4).

⁵As in Model 1, one might suspect that the number of isomorphs for the two equilibria might be driving the finding that the Box is more probable. However, the Box has fewer isomorphs (3) than the 3-Branch (4).