Abrupt transition in the structural formation of interconnected networks

By Filippo Radicchi, Alex Arenas. Nature Physics, 2013

288 citations recorded by the source corpus.

Real-world networks are rarely isolated. A model of an interdependent network of networks shows that an abrupt phase transition occurs when interconnections between independent networks are added. This study also suggests ways to minimize the danger of abrupt structural changes to real networks. Our world is linked by a complex mesh of networks through which information, people and goods flow. These networks are interdependent on each other, and present structural and dynamical features1,2,3,4,5,6 different from those observed in isolated networks7,8,9. Although examples of such dissimilar properties are becoming more abundant—such as in diffusion, robustness and competition—it is not yet clear where these differences are rooted. Here we show that the process of building independent networks into an interconnected network of networks undergoes a structurally sharp transition as the interconnections are formed. Depending on the relative importance of inter- and intra- layer connections, we find that the entire interdependent system can be tuned between two regimes: in one regime, the various layers are structurally decoupled and they act as independent entities; in the other regime, network layers are indistinguishable and the whole system behaves as a single-level network. We analytically show that the transition between the two regimes is discontinuous even for finite-size networks. Thus, any real-world interconnected system is potentially at risk of abrupt changes in its structure, which may manifest new dynamical properties.

Subfields: Economics and Econometrics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/713afd8a53e36fabcfee1013438d866df2778f85

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Citations in the corpus

Network resilience (2020, background): “As discussed in Chapter 6, studies focusing mainly on the structural integrity and robustness have been carried out already [14, 825].”
Random walks and diffusion on networks (2016, background): “re p i (t) is the probability that a random walker visits the ith node in the th layer. The normalization is given by P ‘ max i=1 N i=1 p (t) = 1. Consider the case of two layers and D x D 12 = D 21 [237, 239]. Equation (109) is written concisely as dp(t) dt = p(t)L; (110) where p(t) = (p1 1 (t); p1”
Ranking in interconnected multilayer networks reveals versatile nodes (2013, background): “It is important to discuss the difference between the topological structure which represents the core of this study, namely interconnected multilayer networks [4, 5, 6, 7, 8, 9, 10], and other multilayer structures which have been named multiplexes in the past and have been the subject of recent stu”
Multilayer Analysis and Visualization of Networks (2014, background): “For example, there have been numerous studies to attempt to understand how interdependencies (e.g., [37, 38]), multilayer structures (e.g., [39, 40]), dynamics (e.g., [41, 42]), and control (e.g., [43]) can improve understanding of complex interacting systems.”
Human mobility: Models and applications (2017, background): “This leads to new features such as congestion [207], change in the navigability of the network subject to disruptions [208, 209], produces new dynamic regimes that are absent in monolayers [210] and abrupt reactions to minimal topological changes [211].”
The structure and dynamics of multilayer networks (2014, background): “[96] as a structural transition from a decoupled regime (inwhich layers behave as independent) to a systemic regime (in which layers are indistinguishable).”
Synchronization in complex networks and its application - A survey of recent advances and challenges (2014, background): “The second smallest eigenvalue of the supra-Laplacian matrix L is that given by k2ðLÞ ¼ 2p; if p 6 p ; 6 12 k2ðL1 þ L2Þ; if p P p ; ( ð24Þ where p is the critical value at which the transition of the crossing between two distinct behaviors of k2 occurs (Radicchi & Arenas, 2013).”
Multilayer networks (2013, background): “As we have illustrated above, the study of coupled-cell networks has been very useful for illuminating rich bifurcation phenomena, and additional studies of such phenomena — as well as spiritually similar studies of rich, generic phase-transition phenomena that can occur in multilayer networks [271,”