Adaptive networks are becoming common tools to describe different kinds of systems: from social networks to biological networks, from theoretical synchronization approaches to economic applications. As specified in the clear introduction of this book, adaptive networks account for the need to combine the dynamics on network, recently analyzed in various fields (e.g., opinion dynamics, epidemics, innovation diffusion, and game theory), with the dynamics of the network itself. Combining these two kinds of dynamics becomes extremely important when the time scales of the phenomena taking place on the network are comparable with those of the network dynamics. A double feedback can be in fact identified in such cases: the network topology influences the dynamical processes on the nodes and simultaneously, the states of the nodes (derived by the dynamics) generate a consequent re-shape of the network.
The book contains an exhaustive overview of various examples of realistic adaptive networks, some theoretical arguments on their behaviour and some methodological tools that can be applied in various situations. It contains 14 contributions by influential authors in the field, divided in five main categories: Real-world examples of adaptive networks, Self-Organization of adaptive networks, Contact processes and epidemiology on adaptive networks, Social Games on adaptive networks and Graph-Rewiring-Based Approach.
I will analyze separately the single sections trying to show the different levels of importance that this kind of studies can have for the JASSS community. My overall opinion is that the fact that the book contributors have a different disciplinary background gives to this book an interesting inter-disciplinary flavour that modellers in any field will appreciate.
Real-world examples of adaptive networks
This section presents examples of adaptive networks from real data. It consists of three contributions in different topics. While the first two mainly deal with social networks, the last one regards biological structures.
The first chapter (by Barabasi et al.) presents adaptive networks based on community structure. The authors have elaborated an algorithm to identify community structures in large networks that is applied against real data gathered by a mobile phone network and a co-authorship network. They also provide a model to explain the evolution of such structures and compare the model with the real data. The second paper (by Braha and Bar-Yam) zeros in on the centrality of a node and the concept of "hub" in the case of an e-mail network in a university. They authors show how these concepts assume completely different meanings in static and adaptive networks. The last chapter /by Fricher et al.) regards biological networks. In particular, it describes the growth of Mycelial fungi observed in certain laboratory experiments. In this case, the fungi explores the space looking for nutrients with a simultaneous adaptive optimization of the network for the transport of food.
Self-Organization of adaptive networks
This section analyzes the extension of the concept of Self Organized Criticality (SOC) in relation with adaptive networks. SOC is a very important discovery in statistical physics since it is a means to explain the mechanism by which complexity arises in many different systems governed by local simple rules. For instance, it is applied in different fields like geophysics, evolutionary biology, ecology, and economy, to name a few. This section consists of four contributions. The first two (by Rohlf and Bornholdt and by Caldarelli and Garlaschelli) present the emergence of self-organization in different kinds of adaptive networks. The third one (by Ito and Kanaka) presents how different kinds of nodes can emerge from an initially homogeneous state. Finally, the last one (by Chen and Kurths) presents some results on synchronization on adaptive networks. Though extremely interesting for their innovative results, these chapters are far from the interests of the JASSS community, because of their too much theoretical approach.
Contact processes and epidemiology on adaptive networks
This section focuses on different kinds of processes that take place on adaptive social networks. The first contribution (by Gross) reviews some important papers describing opinion dynamics and epidemic spreading on co-evolving structures. The second one (by Shaw and Schwartz) introduces a more complex epidemic model, using moment approximation techniques. Both contributions are very clear and well written and provide a very useful starting point for those modellers who want to develop models that couple dynamical processes on a network with topological dynamics.
Social Games on adaptive networks
This section presents various types of repeated social games where the players are nodes of adaptive networks. The rules that evolve the network topology depend on the payoffs of the players in the previous game. The first contribution (by Skyrms and Pemantle) suggests a strongly mathematical viewpoint. For some coordination games, e.g., the Friends and the Stag Hunting Game, the authors explore the co-evolution of network topology with strategy. They show, in particular, that the prevalent strategy is strongly dependent on the timing of the adaptation process of the network. The second one (by Traulsen, Santos and Pacheco) is quite different in that it works out a different type of formulation, based on mean field approach and numerical simulation. The authors consider different classes of 2-players evolutionary games. Like in the previous case, the results show how the timing of the linking dynamics can change the nature of the game. The last chapter (by Holme and Ghoshal) is a bit different since it treats a game where players try to optimize their position in the network, i.e., the diplomat's dilemma. In this case, the expected payoff for the players is therefore connected with the local topology of the network in a direct way. Though these three approaches present sound differences among each others, taken all together, they can give to the reader a comprehensive idea of the argument.
Graph-Rewiring-Based Approach
The last section provides some examples that extend the concept of cellular automata to a dynamic contest, with crucial benefits for the description of the behaviour of complex systems. In the first contribution, Tomita, Kurosawa and Murata show how different network topologies can emerge by applying different sets of local graph-rewriting rules in cellular automata. In the second one, Sayama and Laramee propose a new modelling framework called "Generative network automata". This framework integrates the state transitions and the topology transformation into a unified computational framework. My opinion is that this section can be of great interest for modellers who wants to enter this research field, since it provides basic tools that can be applied in many different situations.