Evolving Complex Network Research Articles

Retinal waves in adaptive rewiring networks orchestrate convergence and divergence in the visual system.

Spontaneous retinal wave activity shaping the visual system is a complex neurodevelopmental phenomenon. Retinal ganglion cells are the hubs through which activity diverges throughout the visual system. We consider how these divergent hubs emerge, using an adaptively rewiring neural network model. Adaptive rewiring models show in a principled way how brains could achieve their complex topologies. Modular small-world structures with rich-club effects and circuits of convergent-divergent units emerge as networks evolve, driven by their own spontaneous activity. Arbitrary nodes of an initially random model network were designated as retinal ganglion cells. They were intermittently exposed to the retinal waveform, as the network evolved through adaptive rewiring. A significant proportion of these nodes developed into divergent hubs within the characteristic complex network architecture. The proportion depends parametrically on the wave incidence rate. Higher rates increase the likelihood of hub formation, while increasing the potential of ganglion cell death. In addition, direct neighbors of designated ganglion cells differentiate like amacrine cells. The divergence observed in ganglion cells resulted in enhanced convergence downstream, suggesting that retinal waves control the formation of convergence in the lateral geniculate nuclei. We conclude that retinal waves stochastically control the distribution of converging and diverging activity in evolving complex networks.

A look at financial dependencies by means of econophysics and financial economics

This is a review about financial dependencies which merges efforts in econophysics and financial economics during the last few years. We focus on the most relevant contributions to the analysis of asset markets’ dependencies, especially correlational studies, which in our opinion are beneficial for researchers in both fields. In econophysics, these dependencies can be modeled to describe financial markets as evolving complex networks. In particular, we show that a useful way to describe dependencies is by means of information filtering networks that are able to retrieve relevant and meaningful information in complex financial datasets. In financial economics these dependencies can describe asset comovement and spill-overs. In particular, several models are presented that show how network and factor model approaches are related to modeling of multivariate volatility and asset returns, respectively. Finally, we sketch out how these studies can inspire future research and how they contribute to support researchers in both fields to find a better and a stronger common language.

Local Intrinsic Density Based Community Detection Using Branch-and-Bound and Minimum Spanning Tree

Community detection in complex networks has emerged as a fundamental research area during the last decade. Traditional community detection is primarily based on static techniques, which are neither practicable regarding limited resources nor appropriate for the evolving complex networks. Dynamically updating the community structures, getting accurate and real-time results are vital constraints for analyzing evolving networks, hence in our research, we take these possibilities into consideration. Our work proposes a novel community detection approach BBmst inspired by the original branch-and-bound (BB) concept for label propagation and a Minimum Spanning Tree (MST) to measure the dissimilarity between nodes in graphs. These proposed methods consist of four phases: finding of the local intrinsic density called core or granule of the community, label propagation with BB, an MST is employed to segregate the detected communities and finally a modularity-based community merging is performed. The performance of our proposed method is assessed against a few well-known community detectors on real-world social networks concerning various validity measures. Results demonstrated our proposed method superiority over current community detectors and showed a considerable trade-off between cluster accuracy and quality.

The Sensitivity of Community Extra-Structural Features on Event Prediction in Dynamic Social Networks

A dynamic Online Social Network is a special type of evolving complex network in which changes occur over time. The structure of a community may change over time due to the relationship changes between its members or with other communities. This is known as a community event. In this paper, we discussed the effect of important individual community features and the lengths of adequate time intervals considered in the analysis of the behavior of social networks on the prediction accuracy of each event. Furthermore, we introduced the extra-structural features as global social network features to justify the relationship between the lengths of time intervals used in the model training by using the best prediction accuracy of events. We found a relationship between the scale of network dynamics and the length of time intervals for observing the spread and decomposed events. Finally, by comparing the accuracy of the model based on time interval length which investigated based on cps-value in this study and using the Event Prediction in Dynamic Social Network (EPDSN) model, the hypothesis of a reverse relationship between cps growth rate and time interval length to obtain better prediction accuracy for both the spread and decomposed events.

Temporal link prediction in directed networks based on self-attention mechanism

The development of graph neural networks (GCN) makes it possible to learn structural features from evolving complex networks. Even though a wide range of realistic networks are directed ones, few existing works investigated the properties of directed and temporal networks. In this paper, we address the problem of temporal link prediction in directed networks and propose a deep learning model based on GCN and self-attention mechanism, namely TSAM. The proposed model adopts an autoencoder architecture, which utilizes graph attentional layers to capture the structural feature of neighborhood nodes, as well as a set of graph convolutional layers to capture motif features. A graph recurrent unit layer with self-attention is utilized to learn temporal variations in the snapshot sequence. We run comparative experiments on four realistic networks to validate the effectiveness of TSAM. Experimental results show that TSAM outperforms most benchmarks under two evaluation metrics.

T-GAN: A deep learning framework for prediction of temporal complex networks with adaptive graph convolution and attention mechanism

Complex network is graph network with non-trivial topological features often occurring in real systems, such as video monitoring networks, social networks and sensor networks. While there is growing research study on complex networks, the main focus has been on the analysis and modeling of large networks with static topology. Predicting and control of temporal complex networks with evolving patterns are urgently needed but have been rarely studied. In view of the research gaps we are motivated to propose a novel end-to-end deep learning based network model, which is called temporal graph convolution and attention (T-GAN) for prediction of temporal complex networks. To joint extract both spatial and temporal features of complex networks, we design new adaptive graph convolution and integrate it with Long Short-Term Memory (LSTM) cells. An encoder-decoder framework is applied to achieve the objectives of predicting properties and trends of complex networks. And we proposed a dual attention block to improve the sensitivity of the model to different time slices. Our proposed T-GAN architecture is general and scalable, which can be used for a wide range of real applications. We demonstrate the applications of T-GAN to three prediction tasks for evolving complex networks, namely, node classification, feature forecasting and topology prediction over 6 open datasets. Our T-GAN based approach significantly outperforms the existing models, achieving improvement of more than 4.7% in recall and 25.1% in precision. Additional experiments are also conducted to show the generalization of the proposed model on learning the characteristic of time-series images. Extensive experiments demonstrate the effectiveness of T-GAN in learning spatial and temporal feature and predicting properties for complex networks.

Synchronization in Time-Varying and Evolving Complex Networks

In this contribution, we present the synchronization in dynamical complex networks with varying couplings. We identify two kinds of variations—(i) Non autonomous (Time-varying) couplings: where the coupling strength depends exclusively on time, (ii) Autonomous or Varying couplings (evolution) where the coupling strength depends on the behavior of the interconnected systems. The coupling strength in (i) is exogenous whereas in (ii) the coupling strength is endogenous and is defined by the states of the systems in the nodes. The exponential stability of the synchronization is ensured for the non autonomous couplings, due to the imposition of the coupling strength. Whereas, in the case of evolutionary couplings the exponential stability of the synchronization is not guaranteed for all time, due to the couplings are not controlled or imposed. We present an overview of these features in complex networks and illustrated by means of numerical examples.

Generating Fibonacci-model as evolution of networks with vertex-velocity and time-memory

The problem of how to clearer account for the significant evolutional mechanism gradually driving seemingly random complex networks into ones that have a few typical characters is of great interest in various science communities. Such discussed characters include small-world property, scale-free feature, and self-similarity, etc. However, most of previously generated models have no time memory, that is, the probability for each old vertex i of degree ki to obtain a new link from young vertex does only depend on its current degree. To address this issue, in this paper, we propose a class of prototype of evolving complex network models based on the additional feature, i.e., time memory. In contrast with presented models lacking of time memory, we can find that our model still follows power-law form of vertex-degree distribution and has almost the smallest diameter. More interestingly, this diameter of our model does not increase continuously with the development of model over time, but has discontinuity growth. From the generalization point of view, this thought behind the construction of our model can be thought of as a more general fashion in which a large number of published models can be rebuilt. With the validity of our model, it is worth to note that in the growth process of deterministic network models the number m of each existing vertex i obtaining new edges may be proportional to its degree ki, not always an integer multiple of ki. So as to describe and generate more available deterministic models as complex networks, we here introduce another parameter, vertex-velocity, corresponding to dynamic function on networks, which will be carefully discussed in this paper.

The Opinion Dynamics on the Evolving Complex Network by Achlioptas Process

The interactions of opinions on the complex networks are significantly impacted by the structure of the networks. Previous studies of this kind mainly investigated the opinion dynamics on the fixed networks as a kind of synchronization. In this study, we focus on how the opinions evolving on the growing networks. We provide isolated nodes with different initial opinions at the beginning. The Achlioptas Process is introduced to link the nodes eventually. The opinions of two nodes influence each other linearly if there is a link between the two nodes. We establish both random graph and scale-free network in this paper. The finite-size scaling is discussed. We discover explosive transition of the speed for the opinions to achieve a consensus on some networks. Meanwhile, the stability of the networks to suppress the random damage is highly enhanced by the Achlioptas Process which is used to link all the nodes as a network. The encouraging results are obtained on different structures of networks.

Temporal evolution of the spatial covariability of rainfall in South America

The climate of South America exhibits pronounced differences between rainy and dry seasons, associated with specific synoptic features such as the establishment of the South Atlantic convergence zone. Here, we analyze the spatiotemporal correlation structure and in particular teleconnections of daily rainfall associated with these features by means of evolving complex networks. A modification of Pearson’s correlation coefficient is introduced to handle the intricate statistical properties of daily rainfall. On this basis, spatial correlation networks are constructed, and new appropriate network measures are introduced in order to analyze the temporal evolution of the networks’ characteristics. We particularly focus on the identification of coherent areas of similar rainfall patterns and previously unknown teleconnection structures between remote areas. We show that the monsoon onset is characterized by an abrupt transition from erratic to organized regional connectivity that prevails during the monsoon season, while only the onset times themselves exhibit anomalous large-scale organization of teleconnections. Furthermore, we reveal that the two mega-droughts in the Amazon basin were already announced in the previous year by an anomalous behavior of the connectivity structure.

Dynamic of Firework Algorithm Analyzed with Complex Network

In this paper, a visualization of Firework Algorithm (FWA) inner dynamics as an evolving complex network is presented. Recent research in unconventional controlling and simulation of metaheuristic dynamics shows that this kind of visualization technique has been utilized only for algorithms with some social communication or behavior leading to sharing information across the population. However, provided analysis suggests that the network can identify some types of surface of tested functions.

Local rewiring rules for evolving complex networks

The effects of link rewiring are considered for the class of directed networks where each node has the same fixed out-degree. We model a network generated by three mechanisms that are present in various networked systems; growth, global rewiring and local rewiring. During a rewiring phase a node is randomly selected, one of its out-going edges is detached from its destination then re-attached to the network in one of two possible ways; either globally to a randomly selected node, or locally to a descendant of a descendant of the originally selected node. Although the probability of attachment to a node increases with its connectivity, the probability of detachment also increases, the result is an exponential degree distribution with a small number of outlying nodes that have extremely large degree. We explain these outliers by identifying the circumstances for which a set of nodes can grow to very high degree.

The integration/segregation phenomena in evolving complex networks

The integration/segregation phenomena in evolving complex networks

Identification and Evolution of Structurally Dominant Nodes in Protein-Protein Interaction Networks

It is well known that protein-protein interaction (PPI) networks are typical evolving complex networks. Identification of important nodes has been an emerging popular topic in complex networks. Many indexes have been proposed to measure the importance of nodes in complex networks, such as degree, closeness, betweenness, k-shell, clustering coefficient, semi-local centrality, eigenvector centrality. Based on multivariate statistical analysis, through integrating the above indexes and further considering the appearances of nodes in network motifs, this paper aims at developing a new measure to characterize the structurally dominant proteins (SDP) in PPI networks. Moreover, we will further investigate the evolution of the defined dominant nodes in temporal evolving real-world and artificial PPI networks. Our results indicate that the constructed artificial networks have some similar statistical properties as those of the real-world evolving networks. In this case, the artificial PPI networks can be used to further investigate the above evolution characteristics of the real-world evolving networks. Simulation results reveal that SDP in the yeast PPI networks are evolutionary conserved, however, the undominant nodes evolve rapidly. Furthermore, PPI networks are very robust against random mutations, while fragile yet with certain robustness to targeted mutations on SDP. Our investigations shed some light on the future applications of the evolving characteristics of bio-molecular networks, such as reengineering of particular networks for technological, synthetic or pharmacological purposes.

The bounds of heavy-tailed return distributions in evolving complex networks

We consider the evolution of scale-free networks according to preferential attachment schemes and show the conditions for which the exponent characterizing the degree distribution is bounded by upper and lower values. Our framework is an agent model, presented in the context of economic networks of trades, which shows the emergence of critical behavior. Starting from a brief discussion about the main features of the evolving network of trades, we show that the logarithmic return distributions have bounded heavy-tails, and the corresponding bounding exponent values can be derived. Finally, we discuss these findings in the context of model risk.

Sequential detection of temporal communities by estrangement confinement

Temporal communities are the result of a consistent partitioning of nodes across multiple snapshots of an evolving network, and they provide insights into how dense clusters in a network emerge, combine, split and decay over time. To reliably detect temporal communities we need to not only find a good community partition in a given snapshot but also ensure that it bears some similarity to the partition(s) found in the previous snapshot(s), a particularly difficult task given the extreme sensitivity of community structure yielded by current methods to changes in the network structure. Here, motivated by the inertia of inter-node relationships, we present a new measure of partition distance called estrangement, and show that constraining estrangement enables one to find meaningful temporal communities at various degrees of temporal smoothness in diverse real-world datasets. Estrangement confinement thus provides a principled approach to uncovering temporal communities in evolving networks.

Kinetics of node splitting in evolving complex networks

We introduce a collection of complex networks generated by a combination of preferential attachment and a previously unexamined process of “splitting” nodes of degree k into k nodes of degree 1. Four networks are considered, each evolves at each time step by either preferential attachment, with probability p, or splitting with probability 1−p. Two methods of attachment are considered; first, attachment of an edge between a newly created node and an existing node in the network, and secondly by attachment of an edge between two existing nodes. Splitting is also considered in two separate ways; first by selecting each node with equal probability and secondly, selecting the node with probability proportional to its degree. Exact solutions for the degree distributions are found and scale-free structure is exhibited in those networks where the candidates for splitting are chosen with uniform probability, those that are chosen preferentially are distributed with a power law with exponential cut-off.

Effect of Coagulation of Nodes in an Evolving Complex Network

We propose a new type of stochastic network evolution model based on annihilation, creation, and coagulation of nodes, together with the preferential attachment rule. The system reaches a unique quasistatistically steady state in which the distribution of links follows a power law, lifetime of nodes follows an exponential distribution, and the mean number of links grows exponentially with time. The master equation of the model is solved analytically by applying Smoluchowski's coagulation equation for aerosols. The results indicate that coagulation of nodes in complex networks and mean field analysis of aerosols are similar in both the growth dynamics with irreversible processes and in the steady state statistics. We confirm that the basic properties of the model are consistent with the empirical results of a business transaction network having about 1×10(6) firms.

Attack Resilience of the Evolving Scientific Collaboration Network

Stationary complex networks have been extensively studied in the last ten years. However, many natural systems are known to be continuously evolving at the local (“microscopic”) level. Understanding the response to targeted attacks of an evolving network may shed light on both how to design robust systems and finding effective attack strategies. In this paper we study empirically the response to targeted attacks of the scientific collaboration networks. First we show that scientific collaboration network is a complex system which evolves intensively at the local level – fewer than 20% of scientific collaborations last more than one year. Then, we investigate the impact of the sudden death of eminent scientists on the evolution of the collaboration networks of their former collaborators. We observe in particular that the sudden death, which is equivalent to the removal of the center of the egocentric network of the eminent scientist, does not affect the topological evolution of the residual network. Nonetheless, removal of the eminent hub node is exactly the strategy one would adopt for an effective targeted attack on a stationary network. Hence, we use this evolving collaboration network as an experimental model for attack on an evolving complex network. We find that such attacks are ineffectual, and infer that the scientific collaboration network is the trace of knowledge propagation on a larger underlying social network. The redundancy of the underlying structure in fact acts as a protection mechanism against such network attacks.

Multiscale Evolving Complex Network Model of Functional Connectivity in Neuronal Cultures

Cultures of cortical neurons grown on multielectrode arrays exhibit spontaneous, robust, and recurrent patterns of highly synchronous activity called bursts. These bursts play a crucial role in the development and topological self-organization of neuronal networks. Thus, understanding the evolution of synchrony within these bursts could give insight into network growth and the functional processes involved in learning and memory. Functional connectivity networks can be constructed by observing patterns of synchrony that evolve during bursts. To capture this evolution, a modeling approach is adopted using a framework of emergent evolving complex networks and, through taking advantage of the multiple time scales of the system, aims to show the importance of sequential and ordered synchronization in network function.