Information cascades on degree-correlated random networks

The Downside of Heterogeneity: How Established Relations Counteract Systemic Adaptivity in Tasks Assignments

We study the lock-in effect in a network of task assignments. Agents have a heterogeneous fitness for solving tasks and can redistribute unfinished tasks to other agents. They learn over time to whom to reassign tasks and preferably choose agents with higher fitness. A lock-in occurs if reassignments can no longer adapt. Agents overwhelmed with tasks then fail, leading to failure cascades. We find that the probability for lock-ins and systemic failures increase with the heterogeneity in fitness values. To study this dependence, we use the Shannon entropy of the network of task assignments. A detailed discussion links our findings to the problem of resilience and observations in social systems.

Role of lurkers in threshold-driven information spreading dynamics

The threshold model as a classical paradigm for studying information spreading processes has been well studied. The main focuses are on how the underlying social network structure or the size of initial seeds can affect the cascading dynamics. However, the influence of node characteristics has been largely ignored. Here, inspired by empirical observations, we extend the threshold model by taking into account lurking nodes, who rarely interact with their neighbors. In particular, we consider two different scenarios: (i) Lurkers are absolutely silent and never interact with others and (ii) lurkers intermittently interact with their neighborhood with an activity rate p. In the first case, we demonstrate that lurkers may reduce the effective average degree of the underlying network, playing a dual role in spreading dynamics. In the latter case, we find that the stochastic dynamic behavior of lurkers could significantly promote the spread of information. Concretely, slightly raising the activity rate p of lurkers may result in a remarkable increase in the final cascade size. Further increasing p could make nodes become more stable on average, while it is still easy to observe global cascades due to the fluctuations of the effective degree of nodes.

The transsortative structure of networks

Network topologies can be highly non-trivial, due to the complex underlying behaviours that form them. While past research has shown that some processes on networks may be characterized by local statistics describing nodes and their neighbours, such as degree assortativity, these quantities fail to capture important sources of variation in network structure. We define a property called transsortativity that describes correlations among a node's neighbours. Transsortativity can be systematically varied, independently of the network's degree distribution and assortativity. Moreover, it can significantly impact the spread of contagions as well as the perceptions of neighbours, known as the majority illusion. Our work improves our ability to create and analyse more realistic models of complex networks.

Coevolution spreading in complex networks

The propagations of diseases, behaviors and information in real systems are rarely independent of each other, but they are coevolving with strong interactions. To uncover the dynamical mechanisms, the evolving spatiotemporal patterns and critical phenomena of networked coevolution spreading are extremely important, which provide theoretical foundations for us to control epidemic spreading, predict collective behaviors in social systems, and so on. The coevolution spreading dynamics in complex networks has thus attracted much attention in many disciplines. In this review, we introduce recent progress in the study of coevolution spreading dynamics, emphasizing the contributions from the perspectives of statistical mechanics and network science. The theoretical methods, critical phenomena, phase transitions, interacting mechanisms, and effects of network topology for four representative types of coevolution spreading mechanisms, including the coevolution of biological contagions, social contagions, epidemic-awareness, and epidemic-resources, are presented in detail, and the challenges in this field as well as open issues for future studies are also discussed.

Flickering in Information Spreading Precedes Critical Transitions in Financial Markets

As many complex dynamical systems, financial markets exhibit sudden changes or tipping points that can turn into systemic risk. This paper aims at building and validating a new class of early warning signals of critical transitions. We base our analysis on information spreading patterns in dynamic temporal networks, where nodes are connected by short-term causality. Before a tipping point occurs, we observe flickering in information spreading, as measured by clustering coefficients. Nodes rapidly switch between "being in" and "being out" the information diffusion process. Concurrently, stock markets start to desynchronize. To capture these features, we build two early warning indicators based on the number of regime switches, and on the time between two switches. We divide our data into two sub-samples. Over the first one, using receiver operating curve, we show that we are able to detect a tipping point about one year before it occurs. For instance, our empirical model perfectly predicts the Global Financial Crisis. Over the second sub-sample, used as a robustness check, our two statistical metrics also capture, to a large extent, the 2016 financial turmoil. Our results suggest that our indicators have informational content about a future tipping point, and have therefore strong policy implications.

Critical transitions in heterogeneous networks: Loss of low-degree nodes as an early warning signal

A large number of real networks show abrupt phase transition phenomena in response to environmental changes. In this case, cascading phenomena can induce drastic and discontinuous changes in the system state and lead to collapse. Although complex network theory has been used to investigate these drastic events, we are still unable to predict them effectively. We here analyze collapse phenomena by proposing a minimal two-state dynamic on a complex network and introducing the effect of local connectivities on the evolution of network nodes. We find that a heterogeneous system of interconnected components presents a mixed response to stress and can serve as a control indicator. In particular, before the critical transition point is reached a severe loss of low-degree nodes is observed, masked by the minimal failure of higher-degree nodes. Accordingly, we suggest that a significant reduction in less connected nodes can indicate impending global failure.

Degree correlations amplify the growth of cascades in networks

Networks facilitate the spread of cascades, allowing a local perturbation to percolate via interactions between nodes and their neighbors. We investigate how network structure affects the dynamics of a spreading cascade. By accounting for the joint degree distribution of a network within a generating function framework, we can quantify how degree correlations affect both the onset of global cascades and the propensity of nodes of specific degree class to trigger large cascades. However, not all degree correlations are equally important in a spreading process. We introduce a new measure of degree assortativity that accounts for correlations among nodes relevant to a spreading cascade. We show that the critical point defining the onset of global cascades has a monotone relationship to this new assortativity measure. In addition, we show that the choice of nodes to seed the largest cascades is strongly affected by degree correlations. Contrary to traditional wisdom, when degree assortativity is positive, low degree nodes are more likely to generate largest cascades. Our work suggests that it may be possible to tailor spreading processes by manipulating the higher-order structure of networks.

Information filtering by smart nodes in random networks

Diffusion of information in social networks has drawn extensive attention from various scientific communities, with many contagion models proposed to explain related phenomena. In this paper, we present a simple contagion mechanism, in which a node will change its state immediately if it is exposed to the diffusive information. By considering two types of nodes (smart and normal) and two kinds of information (true and false), we study analytically and numerically how smart nodes influence the spreading of information, which leads to information filtering. We find that for randomly distributed smart nodes, the spreading dynamics over random networks with Poisson degree distribution and power-law degree distribution (with relatively small cutoffs) can both be described by the same approximate mean-field equation. Increasing the heterogeneity of the network may elicit more deviations, but not much. Moreover, we demonstrate that more smart nodes make the filtering effect on a random network better. Finally, we study the efficacy of different strategies of selecting smart nodes for information filtering.

Framework for cascade size calculations on random networks

We present a framework to calculate the cascade size evolution for a large class of cascade models on random network ensembles in the limit of infinite network size. Our method is exact and applies to network ensembles with almost arbitrary degree distribution, degree-degree correlations, and, in case of threshold models, for arbitrary threshold distribution. With our approach, we shift the perspective from the known branching process approximations to the iterative update of suitable probability distributions. Such distributions are key to capture cascade dynamics that involve possibly continuous quantities and that depend on the cascade history, e.g., if load is accumulated over time. As a proof of concept, we provide two examples: (a) Constant load models that cover many of the analytically tractable casacade models, and, as a highlight, (b) a fiber bundle model that was not tractable by branching process approximations before. Our derivations cover the whole cascade dynamics, not only their steady state. This allows us to include interventions in time or further model complexity in the analysis.

Explicit size distributions of failure cascades redefine systemic risk on finite networks

How big is the risk that a few initial failures of nodes in a network amplify to large cascades that span a substantial share of all nodes? Predicting the final cascade size is critical to ensure the functioning of a system as a whole. Yet, this task is hampered by uncertain and missing information. In infinitely large networks, the average cascade size can often be estimated by approaches building on local tree and mean field approximations. Yet, as we demonstrate, in finite networks, this average does not need to be a likely outcome. Instead, we find broad and even bimodal cascade size distributions. This phenomenon persists for system sizes up to 10⁷ and different cascade models, i.e. it is relevant for most real systems. To show this, we derive explicit closed-form solutions for the full probability distribution of the final cascade size. We focus on two topological limit cases, the complete network representing a dense network with a very narrow degree distribution, and the star network representing a sparse network with a inhomogeneous degree distribution. Those topologies are of great interest, as they either minimize or maximize the average cascade size and are common motifs in many real world networks.

How damage diversification can reduce systemic risk

We study the influence of risk diversification on cascading failures in weighted complex networks, where weighted directed links represent exposures between nodes. These weights result from different diversification strategies and their adjustment allows us to reduce systemic risk significantly by topological means. As an example, we contrast a classical exposure diversification (ED) approach with a damage diversification (DD) variant. The latter reduces the loss that the failure of high degree nodes generally inflict to their network neighbors and thus hampers the cascade amplification. To quantify the final cascade size and obtain our results, we develop a branching process approximation taking into account that inflicted losses cannot only depend on properties of the exposed, but also of the failing node. This analytic extension is a natural consequence of the paradigm shift from individual to system safety. To deepen our understanding of the cascade process, we complement this systemic perspective by a mesoscopic one: an analysis of the failure risk of nodes dependent on their degree. Additionally, we ask for the role of these failures in the cascade amplification.

Trend-driven information cascades on random networks

Threshold models of global cascades have been extensively used to model real-world collective behavior, such as the contagious spread of fads and the adoption of new technologies. A common property of those cascade models is that a vanishingly small seed fraction can spread to a finite fraction of an infinitely large network through local infections. In social and economic networks, however, individuals' behavior is often influenced not only by what their direct neighbors are doing, but also by what the majority of people are doing as a trend. A trend affects individuals' behavior while individuals' behavior creates a trend. To analyze such a complex interplay between local- and global-scale phenomena, I generalize the standard threshold model by introducing a type of node called global nodes (or trend followers), whose activation probability depends on a global-scale trend, specifically the percentage of activated nodes in the population. The model shows that global nodes play a role as accelerating cascades once a trend emerges while reducing the probability of a trend emerging. Global nodes thus either facilitate or inhibit cascades, suggesting that a moderate share of trend followers may maximize the average size of cascades.

Kinetics of Social Contagion

Diffusion of information, behavioral patterns or innovations follows diverse pathways depending on a number of conditions, including the structure of the underlying social network, the sensitivity to peer pressure and the influence of media. Here we study analytically and by simulations a general model that incorporates threshold mechanism capturing sensitivity to peer pressure, the effect of "immune" nodes who never adopt, and a perpetual flow of external information. While any constant, nonzero rate of dynamically introduced spontaneous adopters leads to global spreading, the kinetics by which the asymptotic state is approached shows rich behavior. In particular, we find that, as a function of the immune node density, there is a transition from fast to slow spreading governed by entirely different mechanisms. This transition happens below the percolation threshold of network fragmentation, and has its origin in the competition between cascading behavior induced by adopters and blocking due to immune nodes. This change is accompanied by a percolation transition of the induced clusters.

Effects of random rewiring on the degree correlation of scale-free networks

Random rewiring is used to generate null networks for the purpose of analyzing the topological properties of scale-free networks, yet the effects of random rewiring on the degree correlation are subject to contradicting interpretations in the literature. We comprehensively analyze the degree correlation of randomly rewired scale-free networks and show that random rewiring increases disassortativity by reducing the average degree of the nearest neighbors of high-degree nodes. The effect can be captured by the measures of the degree correlation that consider all links in the network, but not by analogous measures that consider only links between degree peers, hence the potential for contradicting interpretations. We furthermore find that random and directional rewiring affect the topology of a scale-free network differently, even if the degree correlation of the rewired networks is the same. Consequently, the network dynamics is changed, which is proven here by means of the biased random walk.

Cascades in multiplex financial networks with debts of different seniority

The seniority of debt, which determines the order in which a bankrupt institution repays its debts, is an important and sometimes contentious feature of financial crises, yet its impact on systemwide stability is not well understood. We capture seniority of debt in a multiplex network, a graph of nodes connected by multiple types of edges. Here an edge between banks denotes a debt contract of a certain level of seniority. Next we study cascading default. There exist multiple kinds of bankruptcy, indexed by the highest level of seniority at which a bank cannot repay all its debts. Self-interested banks would prefer that all their loans be made at the most senior level. However, mixing debts of different seniority levels makes the system more stable in that it shrinks the set of network densities for which bankruptcies spread widely. We compute the optimal ratio of senior to junior debts, which we call the optimal seniority ratio, for two uncorrelated Erdős-Rényi networks. If institutions erode their buffer against insolvency, then this optimal seniority ratio rises; in other words, if default thresholds fall, then more loans should be senior. We generalize the analytical results to arbitrarily many levels of seniority and to heavy-tailed degree distributions.

Modeling of information diffusion in Twitter-like social networks under information overload

Due to the existence of information overload in social networks, it becomes increasingly difficult for users to find useful information according to their interests. This paper takes Twitter-like social networks into account and proposes models to characterize the process of information diffusion under information overload. Users are classified into different types according to their in-degrees and out-degrees, and user behaviors are generalized into two categories: generating and forwarding. View scope is introduced to model the user information-processing capability under information overload, and the average number of times a message appears in view scopes after it is generated by a given type user is adopted to characterize the information diffusion efficiency, which is calculated theoretically. To verify the accuracy of theoretical analysis results, we conduct simulations and provide the simulation results, which are consistent with the theoretical analysis results perfectly. These results are of importance to understand the diffusion dynamics in social networks, and this analysis framework can be extended to consider more realistic situations.

Default cascades in complex networks: topology and systemic risk

The recent crisis has brought to the fore a crucial question that remains still open: what would be the optimal architecture of financial systems? We investigate the stability of several benchmark topologies in a simple default cascading dynamics in bank networks. We analyze the interplay of several crucial drivers, i.e., network topology, banks' capital ratios, market illiquidity, and random vs targeted shocks. We find that, in general, topology matters only – but substantially – when the market is illiquid. No single topology is always superior to others. In particular, scale-free networks can be both more robust and more fragile than homogeneous architectures. This finding has important policy implications. We also apply our methodology to a comprehensive dataset of an interbank market from 1999 to 2011.

Genetic and environmental factors affecting cryptic variations in gene regulatory networks

BACKGROUND

Cryptic genetic variation (CGV) is considered to facilitate phenotypic evolution by producing visible variations in response to changes in the internal and/or external environment. Several mechanisms enabling the accumulation and release of CGVs have been proposed. In this study, we focused on gene regulatory networks (GRNs) as an important mechanism for producing CGVs, and examined how interactions between GRNs and the environment influence the number of CGVs by using individual-based simulations.

RESULTS

Populations of GRNs were allowed to evolve under various stabilizing selections, and we then measured the number of genetic and phenotypic variations that had arisen. Our results showed that CGVs were not depleted irrespective of the strength of the stabilizing selection for each phenotype, whereas the visible fraction of genetic variation in a population decreased with increasing strength of selection. On the other hand, increasing the number of different environments that individuals encountered within their lifetime (i.e., entailing plastic responses to multiple environments) suppressed the accumulation of CGVs, whereas the GRNs with more genes and interactions were favored in such heterogeneous environments.

CONCLUSIONS

Given the findings that the number of CGVs in a population was largely determined by the size (order) of GRNs, we propose that expansion of GRNs and adaptation to novel environments are mutually facilitating and sustainable sources of evolvability and hence the origins of biological diversity and complexity.

Analysis of complex contagions in random multiplex networks

We study the diffusion of influence in random multiplex networks where links can be of r different types, and, for a given content (e.g., rumor, product, or political view), each link type is associated with a content-dependent parameter ci in [0,∞] that measures the relative bias type i links have in spreading this content. In this setting, we propose a linear threshold model of contagion where nodes switch state if their "perceived" proportion of active neighbors exceeds a threshold τ. Namely a node connected to mi active neighbors and ki-mi inactive neighbors via type i links will turn active if ∑cimi/∑ciki exceeds its threshold τ. Under this model, we obtain the condition, probability and expected size of global spreading events. Our results extend the existing work on complex contagions in several directions by (i) providing solutions for coupled random networks whose vertices are neither identical nor disjoint, (ii) highlighting the effect of content on the dynamics of complex contagions, and (iii) showing that content-dependent propagation over a multiplex network leads to a subtle relation between the giant vulnerable component of the graph and the global cascade condition that is not seen in the existing models in the literature.

The influence of assortativity on the robustness of signal-integration logic in gene regulatory networks

Gene regulatory networks (GRNs) drive the cellular processes that sustain life. To do so reliably, GRNs must be robust to perturbations, such as gene deletion and the addition or removal of regulatory interactions. GRNs must also be robust to genetic changes in regulatory regions that define the logic of signal-integration, as these changes can affect how specific combinations of regulatory signals are mapped to particular gene expression states. Previous theoretical analyses have demonstrated that the robustness of a GRN is influenced by its underlying topological properties, such as degree distribution and modularity. Another important topological property is assortativity, which measures the propensity with which nodes of similar connectivity are connected to one another. How assortativity influences the robustness of the signal-integration logic of GRNs remains an open question. Here, we use computational models of GRNs to investigate this relationship. We separately consider each of the three dynamical regimes of this model for a variety of degree distributions. We find that in the chaotic regime, robustness exhibits a pronounced increase as assortativity becomes more positive, while in the critical and ordered regimes, robustness is generally less sensitive to changes in assortativity. We attribute the increased robustness to a decrease in the duration of the gene expression pattern, which is caused by a reduction in the average size of a GRN's in-components. This study provides the first direct evidence that assortativity influences the robustness of the signal-integration logic of computational models of GRNs, illuminates a mechanistic explanation for this influence, and furthers our understanding of the relationship between topology and robustness in complex biological systems.

Decelerated spreading in degree-correlated networks

While degree correlations are known to play a crucial role for spreading phenomena in networks, their impact on the propagation speed has hardly been understood. Here we investigate a tunable spreading model on scale-free networks and show that the propagation becomes slow in positively (negatively) correlated networks if nodes with a high connectivity locally accelerate (decelerate) the propagation. Examining the efficient paths offers a coherent explanation for this result, while the k-core decomposition reveals the dependence of the nodal spreading efficiency on the correlation. Our findings should open new pathways to delicately control real-world spreading processes.

Dynamic theory of cascades on finite clustered random networks with a threshold rule

Cascade dynamics on networks are usually analyzed statically to determine existence criteria for cascades. Here, the Watts model of threshold dynamics on random Erdos-Rényi networks is analyzed to determine the dynamic time evolution of cascades. The network is assumed to have a specific finite number of nodes n and is not assumed to be treelike. All combinations of threshold ϕ, network average nodal degree z, and seed sizes |S| from a single node up are included. The analysis permits study of network size effects and increased clustering coefficient. Several size effects not found by infinite network theory are predicted by the analysis and confirmed by simulations. In the region of ϕ and z where a single node can start a cascade, cascades are expanding, in the sense that each step flips a larger group than the previous step did. We show that this region extends to larger values of z than predicted by infinite network analyses. In the region where larger seeds are needed (size proportional to n), cascades begin by contracting: at the outset, each step flips fewer nodes than the previous step, but eventually the process reverses and becomes expanding. A critical mass that grows during the cascade beyond an easily-calculated threshold is identified as the cause of this reversal.