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Full-Text Articles in Physics
Entropy Measures For Complex Networks: Toward An Information Theory Of Complex Topologies, Kartik Anand, Ginestra Bianconi
Entropy Measures For Complex Networks: Toward An Information Theory Of Complex Topologies, Kartik Anand, Ginestra Bianconi
Ginestra Bianconi
The quantification of the complexity of networks is, today, a fundamental problem in the physics of complex systems. A possible roadmap to solve the problem is via extending key concepts of information theory to networks. In this paper we propose how to define the Shannon entropy of a network ensemble and how it relates to the Gibbs and von Neumann entropies of network ensembles. The quantities we introduce here will play a crucial role for the formulation of null models of networks through maximum-entropy arguments and will contribute to inference problems emerging in the field of complex networks.
Critical Fluctuations In Spatial Complex Networks, Serena Bradde, Fabio Caccioli, Luca Dall'asta, Ginestra Bianconi
Critical Fluctuations In Spatial Complex Networks, Serena Bradde, Fabio Caccioli, Luca Dall'asta, Ginestra Bianconi
Ginestra Bianconi
An anomalous mean-field solution is known to capture the non trivial phase diagram of the Ising model in annealed complex networks. Nevertheless the critical fluctuations in random complex networks remain mean-field. Here we show that a break-down of this scenario can be obtained when complex networks are embedded in geometrical spaces. Through the analysis of the Ising model on annealed spatial networks, we reveal in particular the spectral properties of networks responsible for critical fluctuations and we generalize the Ginsburg criterion to complex topologies.
Bose-Einstein Condensation In Complex Networks, Ginestra Bianconi, Albert-László Barabási
Bose-Einstein Condensation In Complex Networks, Ginestra Bianconi, Albert-László Barabási
Ginestra Bianconi
The evolution of many complex systems, including the World Wide Web, business, and citation networks, is encoded in the dynamic web describing the interactions between the system's constituents. Despite their irreversible and nonequilibrium nature these networks follow Bose statistics and can undergo Bose-Einstein condensation. Addressing the dynamical properties of these nonequilibrium systems within the framework of equilibrium quantum gases predicts that the "first-mover-advantage," "fit-get-rich," and "winner-takes-all" phenomena observed in competitive systems are thermodynamically distinct phases of the underlying evolving networks.