Common adversaries form alliances: modelling complex networks via anti-transitivity

Anti-transitivity captures the notion that enemies of enemies are friends, and arises naturally in the study of adversaries in social networks and in the study of conflicting nation states or organizations. We present a simplified, evolutionary model for anti-transitivity influencing link formation in complex networks, and analyze the model's network dynamics. The Iterated Local Anti-Transitivity (or ILAT) model creates anti-clone nodes in each time-step, and joins anti-clones to the parent node's non-neighbor set. The graphs generated by ILAT exhibit familiar properties of complex networks such as densification, short distances (bounded by absolute constants), and bad spectral expansion. We determine the cop and domination number for graphs generated by ILAT, and finish with an analysis of their clustering coefficients. We interpret these results within the context of real-world complex networks and present open problems

Firefighting as a game

The Firefighter Problem was proposed in 1995 [16] as a deterministic discrete-time model for the spread (and containment) of a fire. Its applications reach from real fires to the spreading of diseases and the containment of floods. Furthermore, it can be used to model the spread of computer viruses or viral marketing in communication networks. In this work, we study the problem from a game-theoretical perspective. Such a context seems very appropriate when applied to large networks, where entities may act and make decisions based on their own interests, without global coordination. We model the Firefighter Problem as a strategic game where there is one player for each time step who decides where to place the firefighters. We show that the Price of Anarchy is linear in the general case, but at most 2 for trees. We prove that the quality of the equilibria improves when allowing coalitional cooperation among players. In general, we have that the Price of Anarchy is in T(n/k) where k is the coalition size. Furthermore, we show that there are topologies which have a constant Price of Anarchy even when constant sized coalitions are considered.Peer ReviewedPostprint (author’s final draft

Information diffusion on the iterated local transitivity model of online social networks

We study a recently introduced deterministic model of competitive information diffusion on the Iterated Local Transitivity (ILT) model of Online Social Networks (OSNs). In particular, we show that, for 2 competing agents, an independent Nash Equilibrium (N.E.) on the initial graph remains a N.E. for all subsequent times. We also describe an example showing that this conclusion does not hold for general N.E. in the ILT process