Phenomenon In Complex Networks Research Articles

Two-step and explosive synchronization in frequency-weighted Kuramoto model

We explore the dynamics of interacting phase oscillators in the generalized Kuramoto model with frequency-weighted couplings, focusing on the interplay of frequency distribution and network topology on the nature of transition to synchrony. We explore the impact of heterogeneity in the network topology and the frequency distribution. Our analysis includes unimodal (Gaussian, truncated Gaussian, and uniform) and bimodal frequency distributions. For a unimodal Gaussian distribution, we observe that in comparison to fully-connected network, the competition between topological and dynamical hubs hinders the transition to synchrony in the scale-free network, though explosive synchronization eventually happens. However, in the absence of very large frequencies, the transition is gradual. While uniform frequency distributions lead to explosive synchronization. In bimodal distributions, narrow distribution produce a two-step transition. In this case, central frequencies dominate the dynamics, overshadowing the topological features of the network. For wider bimodal distributions, scale-free network exhibits a gradual increase in the order parameter, whereas in fully-connected networks a first-order transition happens. These results specifically elucidate the mechanisms driving two-step and explosive synchronization in frequency-weighted Kuramoto models, offering new insights into managing synchronization phenomena in complex networks like power grids, neural systems, and social systems.

Critical phenomena in complex networks: from scale-free to random networks

Critical phenomena in complex networks: from scale-free to random networks

Ranking cliques in higher-order complex networks.

Traditional network analysis focuses on the representation of complex systems with only pairwise interactions between nodes. However, the higher-order structure, which is beyond pairwise interactions, has a great influence on both network dynamics and function. Ranking cliques could help understand more emergent dynamical phenomena in large-scale complex networks with higher-order structures, regarding important issues, such as behavioral synchronization, dynamical evolution, and epidemic spreading. In this paper, motivated by multi-node interactions in a topological simplex, several higher-order centralities are proposed, namely, higher-order cycle (HOC) ratio, higher-order degree, higher-order H-index, and higher-order PageRank (HOP), to quantify and rank the importance of cliques. Experiments on both synthetic and real-world networks support that, compared with other traditional network metrics, the proposed higher-order centralities effectively reduce the dimension of a large-scale network and are more accurate in finding a set of vital nodes. Moreover, since the critical cliques ranked by the HOP and the HOC are scattered over a complex network, the HOP and the HOC outperform other metrics in ranking cliques that are vital in maintaining the network connectivity, thereby facilitating network dynamical synchronization and virus spread control in applications.

Distinguishing between different percolation regimes in noisy dynamic networks with an application to epileptic seizures.

In clinical neuroscience, epileptic seizures have been associated with the sudden emergence of coupled activity across the brain. The resulting functional networks-in which edges indicate strong enough coupling between brain regions-are consistent with the notion of percolation, which is a phenomenon in complex networks corresponding to the sudden emergence of a giant connected component. Traditionally, work has concentrated on noise-free percolation with a monotonic process of network growth, but real-world networks are more complex. We develop a class of random graph hidden Markov models (RG-HMMs) for characterizing percolation regimes in noisy, dynamically evolving networks in the presence of edge birth and edge death. This class is used to understand the type of phase transitions undergone in a seizure, and in particular, distinguishing between different percolation regimes in epileptic seizures. We develop a hypothesis testing framework for inferring putative percolation mechanisms. As a necessary precursor, we present an EM algorithm for estimating parameters from a sequence of noisy networks only observed at a longitudinal subsampling of time points. Our results suggest that different types of percolation can occur in human seizures. The type inferred may suggest tailored treatment strategies and provide new insights into the fundamental science of epilepsy.

Synchronization of machine learning oscillators in complex networks

We study synchronization phenomena in complex networks in terms of machine learning oscillators without conventional dynamical equations. Specifically, we adopt an effective machine learning technique known as reservoir computing for modeling dynamical systems of interest. By constructing a coupled configuration, we show that a collection of coupled reservoir oscillators are in identical synchrony over a wider window of coupling strengths. We find that the geometrical and dynamical properties of synchronous orbits are in excellent agreement with that of the learned dynamical system. Remarkably, through this synchronization scheme, we successfully recover an almost identical bifurcation behavior of an observed system via merely its chaotic dynamics. Our work provides an alternative framework for studying synchronization phenomena in nature when only observed data are available.

Anatomical connectivity in children with developmental dyscalculia: A graph theory study.

Current theories postulate that numerical processing depends upon a brain circuit formed by regions and their connections; specialized in the representation and manipulation of the numerical properties of stimuli. It has been suggested that the damage of these network may cause Developmental Dyscalculia (DD): a persistent neurodevelopmental disorder that significantly interferes with academic performance and daily life activities that require mastery of mathematical notions and operations. However, most of the studies on the brain foundations of DD have focused on regions of interest associated with numerical processing, and have not addressed numerical cognition as a complex network phenomenon. The present study explored DD using a Graph Theory network approach. We studied the association between topological measures of integration and segregation of information processing in the brain proposed by Graph Theory; and individual variability in numerical performance in a group of 11 school-aged children with DD (5 of which presented with comorbidity with Developmental Dyslexia, the specific learning disorder for reading) and 17 typically developing peers. A statistically significant correlation was found between the Weber fraction (a measure of numerical representations' precision) and the Clustering Index (a measure of segregation of information processing) in the whole sample. The DD group showed significantly lower Characteristic Path Length (average shortest path length among all pairs of regions in the brain network) compared to controls. Also, differences in critical regions for the brain network performance (hubs) were found between groups. The presence of limbic hubs characterized the DD brain network while right Temporal and Frontal hubs found in controls were absent in the DD group. Our results suggest that the DD may be associated with alterations in anatomical brain connectivity that hinder the capacity to integrate and segregate numerical information.

Does there exist rich-club phenomenon within two steps in complex networks?

Rich club is a special phenomenon in complex networks. It refers to the nodes with high degrees (i.e., rich nodes) that tend to connect with each other to form a “rich club”. This phenomenon exists in many real networks, especially in social networks. However, there are also some networks not having this phenomenon, for example, in many biological networks. Thus, a natural question comes up: do these rich nodes contact with each other through an “agent”? Two rich nodes do not connect directly, but they can establish a connection by an “agent”, i.e., they can connect with each other within two steps. If the rich nodes tend to connect with each other within two steps, we say that they form a “2-step rich club”. The traditional rich club is then called “1-step rich club”. In this paper, we aim to design one method to detect the “2-step rich club” phenomenon in real networks and check whether this new “2-step rich club” phenomenon commonly exists in real networks. We find that most networks with “1-step rich club” will also have “2-step rich club”. However, there also exist few networks having “2-step rich club” structure while not having “1-step rich club” structure. In particular, either 1-step rich-club phenomenon or 2-step rich-club phenomenon exists in most social networks.

Functional rich clubs emerging from the diffusion geometry of complex networks

Real systems are characterized by complex patterns of interactions between their units, by dynamical processes on them, and by the interplay of the two. It is well known that particular structures affect dynamical processes at different scales. Sometimes richly connected units are connected by costly, long-range links. In the brain, hubs form rich clubs for integrating information between different brain regions, and many biological and social networks show this same structural organization. It remains, however, unclear whether this structural organization alone enables a rapid communication between highly connected nodes or whether a functional rich club may emerge as a combination of direct links and longer paths between rich nodes. Here, we identify functional rich clubs through the diffusion geometry, providing a perspective on rich-club phenomena in complex networks. We show that weak structural rich clubs may be functionally stronger, thanks to bridge nodes, while diffusion inside strong structural rich clubs may be damped in modular networks.

Comparative evaluation of community-aware centrality measures

Influential nodes play a critical role in boosting or curbing spreading phenomena in complex networks. Numerous centrality measures have been proposed for identifying and ranking the nodes according to their importance. Classical centrality measures rely on various local or global properties of the nodes. They do not take into account the network community structure. Recently, a growing number of researches have shifted to community-aware centrality measures. Indeed, it is a ubiquitous feature in a vast majority of real-world networks. In the literature, the focus is on designing community-aware centrality measures. However, up to now, there is no systematic evaluation of their effectiveness. This study fills this gap. It allows answering which community-aware centrality measure should be used in practical situations. We investigate seven influential community-aware centrality measures in an epidemic spreading process scenario using the Susceptible-Infected-Recovered (SIR) model on a set of fifteen real-world networks. Results show that generally, the correlation between community-aware centrality measures is low. Furthermore, in a multiple-spreader problem, when resources are available, targeting distant hubs using Modularity Vitality is more effective. However, with limited resources, diffusion expands better through bridges, especially in networks with a medium or strong community structure.

Computing Volumes of Adjacency Polytopes via Draconian Sequences

Adjacency polytopes appear naturally in the study of nonlinear emergent phenomena in complex networks. The ``"PQ-type" adjacency polytope, denoted $\nabla^{\mathrm{PQ}}_G$ and which is the focus of this work, encodes rich combinatorial information about power-flow solutions in sparse power networks that are studied in electric engineering. Of particular importance is the normalized volume of such an adjacency polytope, which provides an upper bound on the number of distinct power-flow solutions.
 In this article we show that the problem of computing normalized volumes for $\nabla^{\mathrm{PQ}}_G$ can be rephrased as counting $D(G)$-draconian sequences where $D(G)$ is a certain bipartite graph associated to the network. We prove recurrences for all networks with connectivity at most $1$ and, for $2$-connected graphs under certain restrictions, we give recurrences for subdividing an edge and taking the join of an edge with a new vertex. Together, these recurrences imply a simple, non-recursive formula for the normalized volume of $\nabla^{\mathrm{PQ}}_G$ when $G$ is part of a large class of outerplanar graphs; we conjecture that the formula holds for all outerplanar graphs. Explicit formulas for several other (non-outerplanar) classes are given. Further, we identify several important classes of graphs $G$ which are planar but not outerplanar that are worth additional study.

Comparison of observer based methods for source localisation in complex networks

In recent years, research on methods for locating a source of spreading phenomena in complex networks has seen numerous advances. Such methods can be applied not only to searching for the “patient zero” in epidemics, but also finding the true sources of false or malicious messages circulating in the online social networks. Many methods for solving this problem have been established and tested in various circumstances. Yet, we still lack reviews that would include a direct comparison of efficiency of these methods. In this paper, we provide a thorough comparison of several observer-based methods for source localisation on complex networks. All methods use information about the exact time of spread arrival at a pre-selected group of vertices called observers. We investigate how the precision of the studied methods depends on the network topology, density of observers, infection rate, and observers’ placement strategy. The direct comparison between methods allows for an informed choice of the methods for applications or further research. We find that the Pearson correlation based method and the method based on the analysis of multiple paths are the most effective in networks with synthetic or real topologies. The former method dominates when the infection rate is low; otherwise, the latter method takes over.

Analytical approach to the generalized friendship paradox in networks with correlated attributes.

One of the interesting phenomena due to the topological heterogeneities in complex networks is the friendship paradox, stating that your friends have on average more friends than you do. Recently, this paradox has been generalized for arbitrary nodal attributes, called a generalized friendship paradox (GFP). In this paper, we analyze the GFP for the networks in which the attributes of neighboring nodes are correlated with each other. The correlation structure between attributes of neighboring nodes is modeled by the Farlie-Gumbel-Morgenstern copula, enabling us to derive approximate analytical solutions of the GFP for three kinds of methods summarizing the neighborhood of the focal node, i.e., mean-based, median-based, and fraction-based methods. The analytical solutions are comparable to simulation results, while some systematic deviations between them might be attributed to the higher-order correlations between nodal attributes. These results help us get deeper insight into how various summarization methods as well as the correlation structure of nodal attributes affect the GFP behavior, hence better understand various related phenomena in complex networks.

The impact of chaotic saddles on the synchronization of complex networks of discrete-time units

A chaotic saddle is a common nonattracting chaotic set well known for generating finite-time chaotic behavior in low and high-dimensional systems. In general, dynamical systems possessing chaotic saddles in their state-space exhibit irregular behavior with duration lengths following an exponential distribution. However, when these systems are coupled into networks the chaotic saddle plays a role in the long-term dynamics by trapping network trajectories for times that are indefinitely long. This process transforms the network’s high-dimensional state-space by creating an alternative persistent desynchronized state coexisting with the completely synchronized one. Such coexistence threatens the synchronized state with vulnerability to external perturbations. We demonstrate the onset of this phenomenon in complex networks of discrete-time units in which the synchronization manifold is perturbed either in the initial instant of time or in arbitrary states of its asymptotic dynamics. The role of topological asymmetries of Erdös–Rényi and Barabási–Albert graphs are investigated. Besides, the required coupling strength for the occurrence of trapping in the chaotic saddle is unveiled.

Actor-network theory and the evolution of complex adaptive supply networks

PurposeCurrent understandings of innovation in construction portray it as linear, deterministic phenomena centered around novel objects and technologies deployed in sequentially-organized supply chains. This study aims to develop an enriched understanding of construction innovation as non-linear, socio-material and dynamic phenomena in complex networks by formulating a novel conceptual apparatus of complex adaptive supply networks (CASNs) expanded through actor-network theory (ANT) concepts.Design/methodology/approachThis combined CASN/ANT apparatus is mobilized in the context of a qualitative case study involving a housing construction supply network in Australia making use of offsite manufacturing (OSM) techniques.FindingsThe study shows that innovative technologies such as novel OSM products can play an important though not necessarily deterministic role in the evolution of CASNs. The study also explicates the process by which the enrollment of non-human agents and the resulting CASN evolution are linked: innovative technologies shape human and non-human interactions in ways that redefine task delegation, role definition and schemas that are fundamental to the shape of CASNs.Originality/valueFindings provide a compelling empirical basis for arguing that CASNs must be conceptualized as heterogeneous systems and that innovation in construction must be understood as non-linear, socio-material and dynamic, rather than linear and driven by technological determinism. The study also interrogates limiting notions of supply chains and supports the notion of alternative inter-organizational forms to understand construction project work.

Systematic evaluation of rationally chosen multitargeted drug combinations: a combination of low doses of levetiracetam, atorvastatin and ceftriaxone exerts antiepileptogenic effects in a mouse model of acquired epilepsy

Epileptogenesis, the gradual process that leads to epilepsy after brain injury or genetic mutations, is a complex network phenomenon, involving a variety of morphological, biochemical and functional brain alterations. Although risk factors for developing epilepsy are known, there is currently no treatment available to prevent epilepsy. We recently proposed a multitargeted, network-based approach to prevent epileptogenesis by rationally combining clinically available drugs and provided first proof-of-concept that this strategy is effective. Here we evaluated eight novel rationally chosen combinations of 14 drugs with mechanisms that target different epileptogenic processes. The combinations consisted of 2-4 different drugs per combination and were administered systemically over 5 days during the latent epileptogenic period in the intrahippocampal kainate mouse model of acquired temporal lobe epilepsy, starting 6 h after kainate. Doses and dosing intervals were based on previous pharmacokinetic and tolerability studies in mice. The incidence and frequency of spontaneous electrographic and electroclinical seizures were recorded by continuous (24/7) video linked EEG monitoring done for seven days at 4 and 12 weeks post-kainate, i.e., long after termination of drug treatment. Compared to vehicle controls, the most effective drug combination consisted of low doses of levetiracetam, atorvastatin and ceftriaxone, which markedly reduced the incidence of electrographic seizures (by 60%; p<0.05) and electroclinical seizures (by 100%; p<0.05) recorded at 12 weeks after kainate. This effect was lost when higher doses of the three drugs were administered, indicating a synergistic drug-drug interaction at the low doses. The potential mechanisms underlying this interaction are discussed. We have discovered a promising novel multitargeted combination treatment for modifying the development of acquired epilepsy.

“The persistent myth of lost hegemony,” revisited: structural power as a complex network phenomenon

This article resuscitates the idea of structural power in world politics by linking it to modern complex network science, presents a theoretical framework for understanding how global structures develop and change, and empirically analyzes the prominence of leading states within global finance, trade, security, and knowledge networks. It argues that the “fitness plus preferential attachment” (FPA) model of complex network evolution provides a logical explanation for the durability of American influence even as some of its advantages in country-level capabilities has eroded, and it introduces a network methodology that is capable of empirically analyzing the organizational complexity that exists within and across domains in world politics. It argues that the rise of China and other emerging powers has been overstated in some ways, but that a redistribution of structural prominence is taking place, in some domains, as emerging markets increase their transnational connections; this has mostly come at the relative expense of Europe, however, rather than the United States.

An On-line Analytical Processing (OLAP) Aggregation Function for Rising Aspects in Collaboration and Social Networks

The overwhelming usage of social and collaboration networks provides the opportunity to analyze evolution of relationships among individuals, like celebrities or co-authors. Discovering such phenomenon in large complex networks is non-trivial due to their large sizes. In this situation, the aggregation functions used in OLAP, are useful to analyze the summarized data. OLAP has successfully proven its worth on multidimensional or complex networks. However, existing aggregations in the current OLAP systems do not produce versatile results in case of social and collaboration networks. This happens because said type of networks have structural connectivity/links among nodes, which cannot be considered by OLAP during its execution. In this situation, a useful discovery in terms of identifying pairs of nodes whose relationships is emerging in recent time, is missed. Such discovery of pairs of nodes is important for various applications such as targeted marketing, future joint partnerships and predicting future correspondence to name a few. In this study, we call such pairs as Rising_Pairs and propose an aggregation function for performing OLAP on network data whose historical information is maintained over a period of times. Using structural information, Rising_Pairs, our proposed aggregation function, discovers the strongly coupled pairs in a network data by emphasizing their recent interactions and attribute similarities. In this way, useful information related to strongly coupled pairs in a network is identified. To verify the effectiveness of our proposal, we implemented it on various types of real-world networks like Facebook, Digital Bibliography and Library Project (DBLP) and Global Positioning System (GPS) trajectory datasets and observed interesting patterns.

Approximation of Interactive Betweenness Centrality in Large Complex Networks

The analysis of real-world systems through the lens of complex networks often requires a node importance function. While many such views on importance exist, a frequently used global node importance measure is betweenness centrality, quantifying the number of times a node occurs on all shortest paths in a network. This centrality of nodes often significantly depends on the presence of nodes in the network; once a node is missing, e.g., due to a failure, other nodes’ centrality values can change dramatically. This observation is, for instance, important when dismantling a network: instead of removing the nodes in decreasing order of their static betweenness, recomputing the betweenness after a removal creates tremendously stronger attacks, as has been shown in recent research. This process is referred to as interactive betweenness centrality. Nevertheless, very few studies compute the interactive betweenness centrality, given its high computational costs, a worst-case runtime complexity of O(N∗∗4) in the number of nodes in the network. In this study, we address the research questions, whether approximations of interactive betweenness centrality can be obtained with reduction of computational costs and how much quality/accuracy needs to be traded in order to obtain a significant reduction. At the heart of our interactive betweenness approximation framework, we use a set of established betweenness approximation techniques, which come with a wide range of parameter settings. Given that we are interested in the top-ranked node(s) for interactive dismantling, we tune these methods accordingly. Moreover, we explore the idea of batch removal, where groups of top-k ranked nodes are removed before recomputation of betweenness centrality values. Our experiments on real-world and random networks show that specific variants of the approximate interactive betweenness framework allow for a speedup of two orders of magnitude, compared to the exact computation, while obtaining near-optimal results. This work contributes to the analysis of complex network phenomena, with a particular focus on obtaining scalable techniques.

Proof-of-concept that network pharmacology is effective to modify development of acquired temporal lobe epilepsy

Epilepsy is a complex network phenomenon that, as yet, cannot be prevented or cured. We recently proposed network-based approaches to prevent epileptogenesis. For proof of concept we combined two drugs (levetiracetam and topiramate) for which in silico analysis of drug-protein interaction networks indicated a synergistic effect on a large functional network of epilepsy-relevant proteins. Using the intrahippocampal kainate mouse model of temporal lobe epilepsy, the drug combination was administered during the latent period before onset of spontaneous recurrent seizures (SRS). When SRS were periodically recorded by video-EEG monitoring after termination of treatment, a significant decrease in incidence and frequency of SRS was determined, indicating antiepileptogenic efficacy. Such efficacy was not observed following single drug treatment. Furthermore, a combination of levetiracetam and phenobarbital, for which in silico analysis of drug-protein interaction networks did not indicate any significant drug-drug interaction, was not effective to modify development of epilepsy. Surprisingly, the promising antiepileptogenic effect of the levetiracetam/topiramate combination was obtained in the absence of any significant neuroprotective or anti-inflammatory effects as indicated by multimodal brain imaging and histopathology. High throughput RNA-sequencing (RNA-seq) of the ipsilateral hippocampus of mice treated with the levetiracetam/topiramate combination showed that several genes that have been linked previously to epileptogenesis, were significantly differentially expressed, providing interesting entry points for future mechanistic studies. Overall, we have discovered a novel combination treatment with promise for prevention of epilepsy.

Onset of synchronization of Kuramoto oscillators in scale-free networks.

Despite the great attention devoted to the study of phase oscillators on complex networks in the last two decades, it remains unclear whether scale-free networks exhibit a nonzero critical coupling strength for the onset of synchronization in the thermodynamic limit. Here, we systematically compare predictions from the heterogeneous degree mean-field (HMF) and the quenched mean-field (QMF) approaches to extensive numerical simulations on large networks. We provide compelling evidence that the critical coupling vanishes as the number of oscillators increases for scale-free networks characterized by a power-law degree distribution with an exponent 2<γ≤3, in line with what has been observed for other dynamical processes in such networks. For γ>3, we show that the critical coupling remains finite, in agreement with HMF calculations and highlight phenomenological differences between critical properties of phase oscillators and epidemic models on scale-free networks. Finally, we also discuss at length a key choice when studying synchronization phenomena in complex networks, namely, how to normalize the coupling between oscillators.