Organization Of Complex Networks Research Articles

Nonparametric inference of higher order interaction patterns in networks

Local interaction patterns play an important role in the structural and functional organization of complex networks. Here we propose a method for obtaining parsimonious decompositions of networks into higher order interactions which can take the form of arbitrary motifs. The method is based on a class of analytically solvable generative models which in combination with non-parametric priors allow us to infer higher order interactions from dyadic graph data without any prior knowledge on the types or frequencies of such interactions. We test the presented approach on simulated data for which we recover the set of underlying higher order interactions to a high degree of accuracy. For empirical networks the method identifies concise sets of atomic subgraphs from within thousands of candidates that cover a large fraction of edges and include higher order interactions of known structural and functional significance. Being based on statistical inference the method also produces a fit of the network to analytically tractable higher order models opening new avenues for the systematic study of higher order interactions.

Nonassortative relationships between groups of nodes are typical in complex networks.

Decomposing a graph into groups of nodes that share similar connectivity properties is essential to understand the organization and function of complex networks. Previous works have focused on groups with specific relationships between group members, such as assortative communities or core-periphery structures, developing computational methods to find these mesoscale structures within a network. Here, we go beyond these two traditional cases and introduce a methodology that is able to identify and systematically classify all possible community types in directed multi graphs, based on the pairwise relationship between groups. We apply our approach to 53 different networks and find that assortative communities are the most common structures, but that previously unexplored types appear in almost every network. A particularly prevalent new type of relationship, which we call a source-basin structure, has information flowing from a sparsely connected group of nodes (source) to a densely connected group (basin). We look in detail at two online social networks-a new network of Twitter users and a well-studied network of political blogs-and find that source-basin structures play an important role in both of them. This confirms not only the widespread appearance of nonassortative structures but also the potential of hitherto unidentified relationships to explain the organization of complex networks.

Nonparametric identification of Kronecker networks

We address the problem to estimate a dynamic network whose edges describe Granger causality relations and whose topology has a Kronecker structure. Such a structure arises in many real networks and allows to understand the organization of complex networks. We propose a kernel-based PEM method to learn such networks. Numerical examples show the effectiveness of the proposed method.

Cross-covariance isolate detect: A new change-point method for estimating dynamic functional connectivity.

Evidence of the non stationary behavior of functional connectivity (FC) networks has been observed in task based functional magnetic resonance imaging (fMRI) experiments and even prominently in resting state fMRI data. This has led to the development of several new statistical methods for estimating this time-varying connectivity, with the majority of the methods utilizing a sliding window approach. While computationally feasible, the sliding window approach has several limitations. In this paper, we circumvent the sliding window, by introducing a statistical method that finds change-points in FC networks where the number and location of change-points are unknown a priori. The new method, called cross-covariance isolate detect (CCID), detects multiple change-points in the second-order (cross-covariance or network) structure of multivariate, possibly high-dimensional time series. CCID allows for change-point detection in the presence of frequent changes of possibly small magnitudes, can assign change-points to one or multiple brain regions, and is computationally fast. In addition, CCID is particularly suited to task based data, where the subject alternates between task and rest, as it firstly attempts isolation of each of the change-points within subintervals, and secondly their detection therein. Furthermore, we also propose a new information criterion for CCID to identify the change-points. We apply CCID to several simulated data sets and to task based and resting state fMRI data and compare it to recent change-point methods. CCID may also be applicable to electroencephalography (EEG), magentoencephalography (MEG) and electrocorticography (ECoG) data. Similar to other biological networks, understanding the complex network organization and functional dynamics of the brain can lead to profound clinical implications. Finally, the R package ccid implementing the method from the paper is available from CRAN.

Extreme vulnerability of high-order organization in complex networks

The robustness and vulnerability of complex networks have always been an important research field, and there are many corresponding phenomena in the real world. For example, natural disasters may destroy power facilities and lead to the fragmentation of the electricity network, resulting in paralysis of network functions. The traditional research on the robustness of networks is to study the connected sub-clusters of low-order (original) networks. Recently, the conception of high-order organization was introduced to complex networks and it was pointed out that the functionality of networks is implemented by their high-order organization. Therefore, when the networks are attacked, one should observe the fragmentation of both low-order networks and high-order networks. In other words, when attacked, even if the low-order network is robust, but the network structure of its corresponding high-order network may have been severely damaged. In this case, it will still be difficult for the networks to maintain its functions. In this paper, based on percolation theory, we conducted random and malicious node and edge attacks on low-order networks. We gradually remove nodes or links from the low-order networks and we then analyze how the network fragmentation of the low-order network and the high-order network change after the attack. The results show that high-order networks are significantly more fragile than low-order networks.

3D microelectrode cluster and stimulation paradigm yield powerful analgesia without noticeable adverse effects.

The lack of satisfactory treatment for persistent pain profoundly impairs the quality of life for many patients. Stimulation of brainstem pain control systems can trigger powerful analgesia, but their complex network organization frequently prevents separation of analgesia from side effects. To overcome this long-standing challenge, we developed a biocompatible gelatin-embedded cluster of ultrathin microelectrodes that enables fine-tuned, high-definition three-dimensional stimulation in periaqueductal gray/dorsal raphe nucleus in awake rats. Analgesia was assessed from both motor reactions and intracortical signals, corresponding to pain-related signals in humans. We could select an individual-specific subset of microelectrodes in each animal that reliably provided strong pain inhibition during normal and hyperalgesia conditions, without noticeable behavioral side effects. Gait, spontaneous cortical activity at rest, and cortical tactile responses were minimally affected, indicating a highly selective action. In conclusion, our developed biocompatible microelectrode cluster and stimulation paradigm reliably enabled powerful, fine-tuned, and selective analgesia without noticeable side effects.

Landscape configuration and composition shape mutualistic and antagonistic interactions among plants, bats, and ectoparasites in human-dominated tropical rainforests

The Atlantic Forest has lost most of its native area due to the ongoing processes of habitat conversion. The suppression of the forest for the implementation mainly of agriculture has created varied environmental mosaics, modifying the native landscapes and affecting natural populations and their ecological interactions. We aimed to evaluate if both landscape configuration and composition interfere distinctively with mutualistic bat-plant and antagonistic bat-ectoparasite interactions. We conducted this study in landscapes composed of an anthropogenic mosaic containing forest patches embedded in a matrix of different monocultures in southern Minas Gerais state, Brazil. We mapped the landscapes to assess the effect of its configuration and composition on the organization of complex networks of ecological interactions. The antagonistic interactions were more affected by the landscape than the mutualistic interactions. Greater forest cover resulted in less diversity of interactions and more specialization of mutualism, whereas in antagonism it was associated with an increased in the nestedness and decrease in the diversity of interactions, modularity, and richness. The higher shape value of the forest patch influenced only antagonism, being correlated with decreased diversity and increased specialization. More diversity of landscape classes resulted in reduced diversity of mutualism, increased nestedness, and decreased modularity in antagonism. We observed that the landscape characteristics influenced differently in different types of interactions, which occurred even when we considered interactions that share taxa, such as the bats that integrate the mutualisms and antagonisms evaluated. These findings demonstrated the importance of managing the entire landscape for the preservation of ecological interactions.

Diffusion geometry of multiplex and interdependent systems.

Complex networks are characterized by latent geometries induced by their topology or by the dynamics on them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by adequate metrics. Random walks, a proxy for a broad spectrum of processes, from simple contagion to metastable synchronization and consensus, have been recently used, Domenico [Phys. Rev. Lett. 118, 168301 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.168301] to define the class of diffusion geometries and pinpoint the functional mesoscale organization of complex networks from a genuine geometric perspective. Here we first extend this class to families of distinct random walk dynamics-including local and nonlocal information-on multilayer networks-a paradigm for biological, neural, social, transportation, and financial systems-overcoming limitations such as the presence of isolated nodes and disconnected components, typical of real-world networks. We then characterize the multilayer diffusion geometry of synthetic and empirical systems, highlighting the role played by different random search dynamics in shaping the geometric features of the corresponding diffusion manifolds.

An architectonic type principle in the development of laminar patterns of cortico-cortical connections

Structural connections between cortical areas form an intricate network with a high degree of specificity. Many aspects of this complex network organization in the adult mammalian cortex are captured by an architectonic type principle, which relates structural connections to the architectonic differentiation of brain regions. In particular, the laminar patterns of projection origins are a prominent feature of structural connections that varies in a graded manner with the relative architectonic differentiation of connected areas in the adult brain. Here we show that the architectonic type principle is already apparent for the laminar origins of cortico-cortical projections in the immature cortex of the macaque monkey. We find that prenatal and neonatal laminar patterns correlate with cortical architectonic differentiation, and that the relation of laminar patterns to architectonic differences between connected areas is not substantially altered by the complete loss of visual input. Moreover, we find that the degree of change in laminar patterns that projections undergo during development varies in proportion to the relative architectonic differentiation of the connected areas. Hence, it appears that initial biases in laminar projection patterns become progressively strengthened by later developmental processes. These findings suggest that early neurogenetic processes during the formation of the brain are sufficient to establish the characteristic laminar projection patterns. This conclusion is in line with previously suggested mechanistic explanations underlying the emergence of the architectonic type principle and provides further constraints for exploring the fundamental factors that shape structural connectivity in the mammalian brain.

P-adic numbers encode complex networks

The Erdős-Rényi (ER) random graph G(n, p) analytically characterizes the behaviors in complex networks. However, attempts to fit real-world observations need more sophisticated structures (e.g., multilayer networks), rules (e.g., Achlioptas processes), and projections onto geometric, social, or geographic spaces. The p-adic number system offers a natural representation of hierarchical organization of complex networks. The p-adic random graph interprets n as the cardinality of a set of p-adic numbers. Constructing a vast space of hierarchical structures is equivalent for combining number sequences. Although the giant component is vital in dynamic evolution of networks, the structure of multiple big components is also essential. Fitting the sizes of the few largest components to empirical data was rarely demonstrated. The p-adic ultrametric enables the ER model to simulate multiple big components from the observations of genetic interaction networks, social networks, and epidemics. Community structures lead to multimodal distributions of the big component sizes in networks, which have important implications in intervention of spreading processes.

Absence of a resolution limit in in-block nestedness

Nestedness refers to a hierarchical organization of complex networks where a given node’s neighbors tend to form a subset of the neighborhoods of higher-degree nodes. Although nestedness has been traditionally interpreted as a macroscopic property that involves all the nodes of the network, recent works have reinterpreted it as a mesoscopic network property, by revealing that interactions in diverse empirical networks are often arranged into blocks that exhibit an internally nested structure. Inspired by the popular modularity function, these works rely on a quality function – called in-block nestedness – that assumes a partition of the nodes into blocks that exhibit an internal nested structure. A potential limitation of this approach is that the optimization of modularity (and related quality functions) notoriously suffers from resolution limits that impair the detectability of small blocks. Yet, we do not know whether the in-block nestedness function may exhibit similar resolution limits. Here, we provide numerical and analytical evidence that the in-block nestedness function lacks a resolution limit, which implies that our capacity to detect correct partitions in networks via its maximization depends solely on the accuracy of the optimization algorithms.

Link-usage asymmetry and collective patterns emerging from rich-club organization of complex networks

In models of excitable dynamics on graphs, excitations can travel in both directions of an undirected link. However, as a striking interplay of dynamics and network topology, excitations often establish a directional preference. Some of these cases of "link-usage asymmetry" are local in nature and can be mechanistically understood, for instance, from the degree gradient of a link (i.e., the difference in node degrees at both ends of the link). Other contributions to the link-usage asymmetry are instead, as we show, self-organized in nature, and strictly nonlocal. This is the case for excitation waves, where the preferential propagation of excitations along a link depends on its orientation with respect to a hub acting as a source, even if the link in question is several steps away from the hub itself. Here, we identify and quantify the contribution of such self-organized patterns to link-usage asymmetry and show that they extend to ranges significantly longer than those ascribed to local patterns. We introduce a topological characterization, the hub-set-orientation prevalence of a link, which indicates its average orientation with respect to the hubs of a graph. Our numerical results show that the hub-set-orientation prevalence of a link strongly correlates with the preferential usage of the link in the direction of propagation away from the hub core of the graph. Our methodology is embedding-agnostic and allows for the measurement of wave signals and the sizes of the cores from which they originate.

Chaotic memetic algorithm and its application for detecting community structure in complex networks.

Community structure is one of the most important topological characteristics of complex networks. Detecting the community structure is a highly challenging problem in analyzing complex networks and it has high significance for understanding the function and organization of complex networks. A wide range of algorithms for this problem uses the maximization of a quality function called modularity. In this paper, a Chaotic Memetic Algorithm is proposed and used to solve the problem of the community structure detection in complex networks. In the proposed algorithm, the combination of the genetic algorithm (global search) and a dedicated local search is used to search the solution space. In addition, to improve the convergence speed and efficiency, in both global search and local search processes, instead of random numbers, chaotic numbers are used. By using chaotic numbers, the population diversity is preserved and it prevents from falling in the local optimum. The experiments on both real-world and synthetic benchmark networks indicate that the proposed algorithm is effective compared with state-of-the-art algorithms.

Multi-scale detection of hierarchical community architecture in structural and functional brain networks.

Community detection algorithms have been widely used to study the organization of complex networks like the brain. These techniques provide a partition of brain regions (or nodes) into clusters (or communities), where nodes within a community are densely interconnected with one another. In their simplest application, community detection algorithms are agnostic to the presence of community hierarchies: clusters embedded within clusters of other clusters. To address this limitation, we exercise a multi-scale extension of a common community detection technique, and we apply the tool to synthetic graphs and to graphs derived from human neuroimaging data, including structural and functional imaging data. Our multi-scale community detection algorithm links a graph to copies of itself across neighboring topological scales, thereby becoming sensitive to conserved community organization across levels of the hierarchy. We demonstrate that this method is sensitive to topological inhomogeneities of the graph’s hierarchy by providing a local measure of community stability and inter-scale reliability across topological scales. We compare the brain’s structural and functional network architectures, and we demonstrate that structural graphs display a more prominent hierarchical community organization than functional graphs. Finally, we build an explicitly multimodal multiplex graph that combines both structural and functional connectivity in a single model, and we identify the topological scales where resting state functional connectivity and underlying structural connectivity show similar versus unique hierarchical community architecture. Together, our results demonstrate the advantages of the multi-scale community detection algorithm in studying hierarchical community structure in brain graphs, and they illustrate its utility in modeling multimodal neuroimaging data.

Abnormal Global Brain Functional Connectivity in Primary Insomnia Patients: A Resting-State Functional MRI Study.

Background: Resting-state functional magnetic resonance imaging (fMRI) studies have uncovered the disruptions of functional brain networks in primary insomnia (PI) patients. However, the etiology and pathogenesis underlying this disorder remains ambiguous, and the insomnia related symptoms are influenced by a complex network organization in the brain. The purpose of this study was to explore the abnormal intrinsic functional hubs in PI patients using a voxel-wise degree centrality (DC) analysis and seed-based functional connectivity (FC) approach.Methods: A total of 26 PI patients and 28 healthy controls were enrolled, and they underwent resting-state fMRI. Degree centrality was measured across the whole brain, and group differences in DC were compared. The peak points, which significantly altered DC between the two groups, were defined as the seed regions and were further used to calculate FC of the whole brain. Later, correlation analyses were performed between the changes in brain function and clinical features.Results: Primary insomnia patients showed DC values lower than healthy controls in the left inferior frontal gyrus (IFG) and middle temporal gyrus (MTG) and showed a higher DC value in the right precuneus. The seed-based analyses demonstrated decreased FC between the left MTG and the left posterior cingulate cortex (PCC), and decreased FC was observed between the right precuneus and the right lateral occipital cortex. Reduced DC in the left IFG and decreased FC in the left PCC were positively correlated with the Pittsburgh sleep quality index and the insomnia severity index.Conclusions: This study revealed that PI patients exhibited abnormal intrinsic functional hubs in the left IFG, MTG, and the right precuneus, as well as abnormal seed-based FC in these hubs. These results contribute to better understanding of how brain function influences the symptoms of PI.

What's in a tide pool? Just as much food web network complexity as in large open ecosystems.

Understanding the fundamental laws that govern complex food web networks over large ecosystems presents high costs and oftentimes unsurmountable logistical challenges. This way, it is crucial to find smaller systems that can be used as proxy food webs. Intertidal rock pool environments harbour particularly high biodiversity over small areas. This study aimed to analyse their food web networks to investigate their potential as proxies of larger ecosystems for food web networks research. Highly resolved food webs were compiled for 116 intertidal rock pools from cold, temperate, subtropical and tropical regions, to ensure a wide representation of environmental variability. The network properties of these food webs were compared to that of estuaries, lakes and rivers, as well as marine and terrestrial ecosystems (46 previously published complex food webs). The intertidal rock pool food webs analysed presented properties that were in the same range as the previously published food webs. The niche model predictive success was remarkably high (73–88%) and similar to that previously found for much larger marine and terrestrial food webs. By using a large-scale sampling effort covering 116 intertidal rock pools in several biogeographic regions, this study showed, for the first time, that intertidal rock pools encompass food webs that share fundamental organizational characteristics with food webs from markedly different, larger, open and abiotically stable ecosystems. As small, self-contained habitats, intertidal rock pools are particularly tractable systems and therefore a large number of food webs can be examined with relatively low sampling effort. This study shows, for the first time that they can be useful models for the understanding of universal processes that regulate the complex network organization of food webs, which are harder or impossible to investigate in larger, open ecosystems, due to high costs and logistical difficulties.

Multiscale mixing patterns in networks

Assortative mixing in networks is the tendency for nodes with the same attributes, or metadata, to link to each other. It is a property often found in social networks, manifesting as a higher tendency of links occurring between people of the same age, race, or political belief. Quantifying the level of assortativity or disassortativity (the preference of linking to nodes with different attributes) can shed light on the organization of complex networks. It is common practice to measure the level of assortativity according to the assortativity coefficient, or modularity in the case of categorical metadata. This global value is the average level of assortativity across the network and may not be a representative statistic when mixing patterns are heterogeneous. For example, a social network spanning the globe may exhibit local differences in mixing patterns as a consequence of differences in cultural norms. Here, we introduce an approach to localize this global measure so that we can describe the assortativity, across multiple scales, at the node level. Consequently, we are able to capture and qualitatively evaluate the distribution of mixing patterns in the network. We find that, for many real-world networks, the distribution of assortativity is skewed, overdispersed, and multimodal. Our method provides a clearer lens through which we can more closely examine mixing patterns in networks.

Higher-order Network Analysis of Fine Particulate Matter (PM2.5) Transport in China at City Level

Specification of PM2.5 transmission characteristics is important for pollution control and policymaking. We apply higher-order organization of complex networks to identify major potential PM2.5 contributors and PM2.5 transport pathways of a network of 189 cities in China. The network we create in this paper consists of major cities in China and contains information on meteorological conditions of wind speed and wind direction, data on geographic distance, mountains, and PM2.5 concentrations. We aim to reveal PM2.5 mobility between cities in China. Two major conclusions are revealed through motif analysis of complex networks. First, major potential PM2.5 pollution contributors are identified for each cluster by one motif, which reflects movements from source to target. Second, transport pathways of PM2.5 are revealed by another motif, which reflects transmission routes. To our knowledge, this is the first work to apply higher-order network analysis to study PM2.5 transport.

Can local-community-paradigm and epitopological learning enhance our understanding of how local brain connectivity is able to process, learn and memorize chronic pain?

The mystery behind the origin of the pain and the difficulty to propose methodologies for its quantitative characterization fascinated philosophers (and then scientists) from the dawn of our modern society. Nowadays, studying patterns of information flow in mesoscale activity of brain networks is a valuable strategy to offer answers in computational neuroscience. In this paper, complex network analysis was performed on the time-varying brain functional connectomes of a rat model of persistent peripheral neuropathic pain, obtained by means of local field potential and spike train analysis. A wide range of topological network measures (14 in total, the code is publicly released at: https://github.com/biomedical-cybernetics/topological_measures_wide_analysis) was employed to quantitatively investigate the rewiring mechanisms of the brain regions responsible for development and upkeep of pain along time, from three hours to 16 days after nerve injury. The time trend (across the days) of each network measure was correlated with a behavioural test for rat pain, and surprisingly we found that the rewiring mechanisms associated with two local topological measure, the local-community-paradigm and the power-lawness, showed very high statistical correlations (higher than 0.9, being the maximum value 1) with the behavioural test. We also disclosed clear functional connectivity patterns that emerged in association with chronic pain in the primary somatosensory cortex (S1) and ventral posterolateral (VPL) nuclei of thalamus. This study represents a pioneering attempt to exploit network science models in order to elucidate the mechanisms of brain region re-wiring and engram formations that are associated with chronic pain in mammalians. We conclude that the local-community-paradigm is a model of complex network organization that triggers a local learning rule, which seems associated to processing, learning and memorization of chronic pain in the brain functional connectivity. This rule is based exclusively on the network topology, hence was named epitopological learning.

Nonlinear growth: an origin of hub organization in complex networks.

Many real-world networks contain highly connected nodes called hubs. Hubs are often crucial for network function and spreading dynamics. However, classical models of how hubs originate during network development unrealistically assume that new nodes attain information about the connectivity (for example the degree) of existing nodes. Here, we introduce hub formation through nonlinear growth where the number of nodes generated at each stage increases over time and new nodes form connections independent of target node features. Our model reproduces variation in number of connections, hub occurrence time, and rich-club organization of networks ranging from protein–protein, neuronal and fibre tract brain networks to airline networks. Moreover, nonlinear growth gives a more generic representation of these networks compared with previous preferential attachment or duplication–divergence models. Overall, hub creation through nonlinear network expansion can serve as a benchmark model for studying the development of many real-world networks.