The possibility to analyze everyday monetary transactions is limited by the scarcity of available data, as this kind information usually considered highly sensitive. Present econophysics models are employed on presumed random networks interacting agents, and only macroscopic properties (e.g. resulting wealth distribution) compared real-world data. In paper, we BitCoin, which a novel digital currency system, where complete list publicly available. Using dataset, reconstruct network...

A dynamical system is controllable if by imposing appropriate external signals on a subset of its nodes, it can be driven from any initial state to desired in finite time. Here we study the impact various network characteristics minimal number driver nodes required control network. We find that clustering and modularity have no discernible impact, but symmetries underlying matching problem produce linear, quadratic or dependence degree correlation coefficients, depending nature correlations....

Synchronization of oscillators, a phenomenon found in wide variety natural and engineered systems, is typically understood through reduction to first-order phase model with simplified dynamics. Here, by exploiting the precision flexibility nanoelectromechanical we examined dynamics ring quasi-sinusoidal oscillators at beyond first order. Beyond order, exotic states synchronization highly complex dynamics, including weak chimeras, decoupled states, traveling waves, inhomogeneous synchronized...

As a fundamental structural transition in complex networks, core percolation is related to wide range of important problems. Yet, previous theoretical studies have been focusing on the classical Erd\H{o}s-R\'enyi random networks with Poisson degree distribution, which are quite unlike many real-world scale-free or fat-tailed distributions. Here we show that can be analytically studied for arbitrary We derive condition and find purely no any exponents. undirected if occurs then it always...

A main focus in economics research is understanding the time series of prices goods and assets. While statistical models using only properties itself have been successful many aspects, we expect to gain a better phenomena involved if can model underlying system interacting agents. In this article, consider history Bitcoin, novel digital currency system, for which complete list transactions available analysis. Using dataset, reconstruct transaction network between users analyze changes...

The paradigm of layered networks is used to describe many real-world systems, from biological social organizations and transportation systems. While recently there has been much progress in understanding the general properties multilayer networks, our how control such systems remains limited. One fundamental aspect that makes this endeavor challenging each layer can operate at a different time scale; thus, we cannot directly apply standard ideas structural theory individual networks. Here...

The control of complex systems is an ongoing challenge complexity research. Recent advances using concepts structural deduce a wide range related properties from the network representation systems. Here, we examine controllability for which timescale dynamics and changes in are comparable. We provide analytical computational tools to study based on temporal characteristics. apply these results investigate controllable subnetwork single input. For generic class model networks, witness phase...

Core percolation is a fundamental structural transition in complex networks related to wide range of important problems. Recent advances have provided us an analytical framework core uncorrelated random with arbitrary degree distributions. Here we apply the tools analysis network controllability. We confirm analytically that emergence bifurcation control coincides formation and structure determines mode network. also derive expression controllability robustness by extending deduction...

Restoring operation of critical infrastructure systems after catastrophic events is an important issue, inspiring work in multiple fields, including network science, civil engineering, and operations research. We consider the problem finding optimal order repairing elements power grids similar infrastructure. Most existing methods either only system structure, potentially ignoring features, or incorporate component level details leading to complex optimization problems with limited...

High-centrality nodes have disproportionate influence on the behavior of a network; therefore controlling such can efficiently steer system to desired state. Existing multiplex centrality measures typically rank assuming layers are qualitatively similar. Many real systems, however, comprised networks heterogeneous in nature, for example, social may both agnostic and affiliative layers. Here, we use aggregation methods identify intervention targets when structure, dynamics, our goals...

Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via architecture their attractors and basins, we investigate patterns switching between distinct trajectories a network synchronized oscillators. Our system, consisting nonlinear amplitude-phase oscillators arranged ring topology with reactive nearest-neighbor coupling, is simple connects directly to experimental realizations. We seek understand how multiple stable states connect each other...

Members of a society interact using variety social behaviors, giving rise to multi-faceted and complex life. For the study animal behavior, quantifying this complexity is critical for understanding impact life on animals' health fitness. Multilayer network approaches, where each interaction type represents different layer network, have potential better capture than single approaches. Calculating individuals' centrality within multilayer can reveal keystone individuals more fully characterize...

The minimum number of inputs needed to control a network is frequently used quantify its controllability. Control linear dynamics through set inputs, however, often has prohibitively large energy requirements and there an inherent trade-off between minimizing the energy. To better understand this trade-off, we study problem identifying input nodes such that controllabililty ensured while restricting length longest chain. chain maximum distance from any node, recent work found reducing...

Social network position in non-human primates has far-reaching fitness consequences. Critically, social networks are both heterogeneous and dynamic, meaning an individual's current is likely to change due intrinsic extrinsic factors. However, our understanding of the drivers changes largely confined opportunistic studies. Experimental research on consequences situ, controlled perturbations limited. Here we conducted a food-based experiment rhesus macaques assess whether allowing individual...

In this Rapid Communication we present an analytic study of sampled networks in the case some important shortest-path sampling models. We formulas for probability edge discovery evolving and a static network model. also show that number discovered edges finite scales much more slowly than predicted by earlier mean-field Finally, calculate degree distribution demonstrate they are analogous to destroyed obtained randomly removing from original network.

Hierarchy of social organization is a ubiquitous property animal and human groups, linked to resource allocation, collective decisions, individual health, even instability. Experimental evidence shows that both intrinsic abilities individuals reinforcement processes impact hierarchies; existing mathematical models, however, focus on the latter. Here, we develop rigorous model incorporates features explore their synergistic effect stability structure hierarchy. For pairwise interactions, show...

The control of complex systems is an ongoing challenge complexity research. Recent advances using concepts structural deduce a wide range related properties from the network representation systems. Here, we examine controllability for which timescale dynamics and changes in are comparable. We provide both analytical computational tools to study based on temporal characteristics. apply these results investigate controllable subnetwork single input, present generic class models, preform...

In physical networks, like the brain or metamaterials, we often observe local bundles, corresponding to locally aligned link configurations. Here introduce a minimal model for bundle formation, modeling networks as non-equilibrium packings of hard-core 3D elongated links. We show that growth is logarithmic in time, stark contrast with algebraic behavior lower dimensional random packing models. Equally important, find this slow kinetics metastable, allowing us analytically predict an due...

Data describing the three-dimensional structure of physical networks is increasingly available, leading to a surge interest in network science explore relationship between shape and connectivity networks. We contribute this effort by standardizing analyzing 15 data sets from different domains. Each made tube-like objects bound together at junction points, which we treat as nodes, with connections them considered links. divide these into three categories: lattice-like networks, trees, linked...

Data describing the three-dimensional structure of physical networks is increasingly available, leading to a surge interest in network science explore relationship between shape and connectivity networks. We contribute this effort by standardizing analyzing 15 data sets from different domains. Each made tube-like objects bound together at junction points, which we treat as nodes, with connections them considered links. divide these into three categories: lattice-like networks, trees, linked...