Community detection in complex networks using extremal optimization

Generative models for two-ground-truth partitions in networks

A myriad of approaches have been proposed to characterize the mesoscale structure of networks most often as a partition based on patterns variously called communities, blocks, or clusters. Clearly, distinct methods designed to detect different types of patterns may provide a variety of answers' to the networks mesoscale structure. Yet even multiple runs of a given method can sometimes yield diverse and conflicting results, producing entire landscapes of partitions which potentially include multiple (locally optimal) mesoscale explanations of the network. Such ambiguity motivates a closer look at the ability of these methods to find multiple qualitatively different "ground truth" partitions in a network. Here we propose the stochastic cross-block model (SCBM), a generative model which allows for two distinct partitions to be built into the mesoscale structure of a single benchmark network. We demonstrate a use case of the benchmark model by appraising the power of stochastic block models (SBMs) to detect implicitly planted coexisting bicommunity and core-periphery structures of different strengths. Given our model design and experimental setup, we find that the ability to detect the two partitions individually varies by SBM variant and that coexistence of both partitions is recovered only in a very limited number of cases. Our findings suggest that in most instances only one-in some way dominating-structure can be detected, even in the presence of other partitions. They underline the need for considering entire landscapes of partitions when different competing explanations exist and motivate future research to advance partition coexistence detection methods. Our model also contributes to the field of benchmark networks more generally by enabling further exploration of the ability of new and existing methods to detect ambiguity in the mesoscale structure of networks.

Link prediction in complex network using information flow

Link prediction in complex networks has recently attracted a great deal of attraction in diverse scientific domains, including social and biological sciences. Given a snapshot of a network, the goal is to predict links that are missing in the network or that are likely to occur in the near future. This problem has both theoretical and practical significance; it not only helps us to identify missing links in a network more efficiently by avoiding the expensive and time consuming experimental processes, but also allows us to study the evolution of a network with time. To address the problem of link prediction, numerous attempts have been made over the recent years that exploit the local and the global topological properties of the network to predict missing links in the network. In this paper, we use parametrised matrix forest index (PMFI) to predict missing links in a network. We show that, for small parameter values, this index is linked to a heat diffusion process on a graph and therefore encodes geometric properties of the network. We then develop a framework that combines the PMFI with a local similarity index to predict missing links in the network. The framework is applied to numerous networks obtained from diverse domains such as social network, biological network, and transport network. The results show that the proposed method can predict missing links with higher accuracy when compared to other state-of-the-art link prediction methods.

Modeling and analysis of affiliation networks with preferential attachment and subsumption

Preferential attachment describes a variety of graph-based models in which a network grows incrementally via the sequential addition of new nodes and edges, and where existing nodes acquire new neighbors at a rate proportional to their degree. Some networks, however, are better described as groups of nodes rather than a set of pairwise connections. These groups are called affiliations, and the corresponding networks affiliation networks. When viewed as graphs, affiliation networks do not necessarily exhibit the power law distribution of node degrees that is typically associated with preferential attachment. We propose a preferential attachment mechanism for affiliation networks that highlights the power law characteristic of these networks when presented as hypergraphs and simplicial complexes. The two representations capture affiliations in similar ways, but the latter offers an intrinsic feature of the model called subsumption, where an affiliation cannot be a subset of another. Our model of preferential attachment has interesting features, both algorithmic and analytic, including implicit preferential attachment (node sampling does not require knowledge of node degrees), a locality property where the neighbors of a newly added node are also neighbors, the emergence of a power law distribution of degrees (defined in hypergraphs and simplicial complexes rather than at a graph level), implicit deletion of affiliations (through subsumption in the case of simplicial complexes), and to some extent a control over the affiliation size distribution. By varying the parameters of the model, the generated affiliation networks can resemble different types of real-world examples, so the framework also serves as a synthetic generation algorithm for simulation and experimental studies.

Non-negative matrix factorization for overlapping community detection in directed weighted networks with sparse constraints

Detecting overlapping communities is essential for analyzing the structure and function of complex networks. However, most existing approaches only consider network topology and overlook the benefits of attribute information. In this paper, we propose a novel attribute-information non-negative matrix factorization approach that integrates sparse constraints and optimizes an objective function for detecting communities in directed weighted networks. Our algorithm updates the basic non-negative matrix adaptively, incorporating both network topology and attribute information. We also add a sparsity constraint term of graph regularization to maintain the intrinsic geometric structure between nodes. Importantly, we provide strict proof of convergence for the multiplication update rule used in our algorithm. We apply our proposed algorithm to various artificial and real-world networks and show that it is more effective for detecting overlapping communities. Furthermore, our study uncovers the intricate iterative process of system evolution toward convergence and investigates the impact of various variables on network detection. These findings provide insights into building more robust and operable complex systems.

Random search immune algorithm for community detection

Community detection is a prominent research topic in Complex Network Analysis, and it constitutes an important research field on all those areas where complex networks represent a powerful interpretation tool for describing and understanding systems involved in neuroscience, biology, social science, economy, and many others. A challenging approach to uncover the community structure in complex network, and then revealing the internal organization of nodes, is Modularity optimization. In this research paper, we present an immune optimization algorithm (opt-IA) developed to detect community structures, with the main aim to maximize the modularity produced by the discovered communities. In order to assess the performance of opt-IA, we compared it with an overall of 20 heuristics and metaheuristics, among which one Hyper-Heuristic method, using social and biological complex networks as data set. Unlike these algorithms, opt-IA is entirely based on a fully random search process, which in turn is combined with purely stochastic operators. According to the obtained outcomes, opt-IA shows strictly better performances than almost all heuristics and metaheuristics to which it was compared; whilst it turns out to be comparable with the Hyper-Heuristic method. Overall, it can be claimed that opt-IA, even if driven by a purely random process, proves to be reliable and with efficient performance. Furthermore, to prove the latter claim, a sensitivity analysis of the functionality was conducted, using the classic metrics NMI, ARI and NVI.

Community detection in brain connectomes with hybrid quantum computing

Recent advancements in network neuroscience are pointing in the direction of considering the brain as a small-world system with an efficient integration-segregation balance that facilitates different cognitive tasks and functions. In this context, community detection is a pivotal issue in computational neuroscience. In this paper we explored community detection within brain connectomes using the power of quantum annealers, and in particular the Leap's Hybrid Solver in D-Wave. By reframing the modularity optimization problem into a Discrete Quadratic Model, we show that quantum annealers achieved higher modularity indices compared to the Louvain Community Detection Algorithm without the need to overcomplicate the mathematical formulation. We also found that the number of communities detected in brain connectomes slightly differed while still being biologically interpretable. These promising preliminary results, together with recent findings, strengthen the claim that quantum optimization methods might be a suitable alternative against classical approaches when dealing with community assignment in networks.

Identifying important nodes in complex networks based on extended degree and E-shell hierarchy decomposition

The identification of important nodes is a hot topic in complex networks. Many methods have been proposed in different fields for solving this problem. Most previous work emphasized the role of a single feature and, as a result, rarely made full use of multiple items. This paper proposes a new method that utilizes multiple characteristics of nodes for the evaluation of their importance. First, an extended degree is defined to improve the classical degree. And E-shell hierarchy decomposition is put forward for determining nodes' position through the network's hierarchical structure. Then, based on the combination of these two components, a hybrid characteristic centrality and its extended version are proposed for evaluating the importance of nodes. Extensive experiments are conducted in six real networks, and the susceptible-infected-recovered model and monotonicity criterion are introduced to test the performance of the new approach. The comparison results demonstrate that the proposed new approach exposes more competitive advantages in both accuracy and resolution compared to the other five approaches.

Improved Link Entropy with Dynamic Community Number Detection for Quantifying Significance of Edges in Complex Social Networks

Discovering communities in complex networks is essential in performing analyses, such as dynamics of political fragmentation and echo chambers in social networks. In this work, we study the problem of quantifying the significance of edges in a complex network, and propose a significantly improved version of the Link Entropy method. Using Louvain, Leiden and Walktrap methods, our proposal detects the number of communities in each iteration on discovering the communities. Running experiments on various benchmark networks, we show that our proposed method outperforms the Link Entropy method in quantifying edge significance. Considering also the computational complexities and possible defects, we conclude that Leiden or Louvain algorithms are the best choice for community number detection in quantifying edge significance. We also discuss designing a new algorithm for not only discovering the number of communities, but also computing the community membership uncertainties.

Large network community detection by fast label propagation

Many networks exhibit some community structure. There exists a wide variety of approaches to detect communities in networks, each offering different interpretations and associated algorithms. For large networks, there is the additional requirement of speed. In this context, the so-called label propagation algorithm (LPA) was proposed, which runs in near-linear time. In partitions uncovered by LPA, each node is ensured to have most links to its assigned community. We here propose a fast variant of LPA (FLPA) that is based on processing a queue of nodes whose neighbourhood recently changed. We test FLPA exhaustively on benchmark networks and empirical networks, finding that it can run up to 700 times faster than LPA. In partitions found by FLPA, we prove that each node is again guaranteed to have most links to its assigned community. Our results show that FLPA is generally preferable to LPA.

Discovering Entities Similarities in Biological Networks Using a Hybrid Immune Algorithm

Disease phenotypes are generally caused by the failure of gene modules which often have similar biological roles. Through the study of biological networks, it is possible to identify the intrinsic structure of molecular interactions in order to identify the so-called “disease modules”. Community detection is an interesting and valuable approach to discovering the structure of the community in a complex network, revealing the internal organization of the nodes, and has become a leading research topic in the analysis of complex networks. This work investigates the link between biological modules and network communities in test-case biological networks that are commonly used as a reference point and which include Protein–Protein Interaction Networks, Metabolic Networks and Transcriptional Regulation Networks. In order to identify small and structurally well-defined communities in the biological context, a hybrid immune metaheuristic algorithm Hybrid-IA is proposed and compared with several metaheuristics, hyper-heuristics, and the well-known greedy algorithm Louvain, with respect to modularity maximization. Considering the limitation of modularity optimization, which can fail to identify smaller communities, the reliability of Hybrid-IA was also analyzed with respect to three well-known sensitivity analysis measures (NMI, ARI and NVI) that assess how similar the detected communities are to real ones. By inspecting all outcomes and the performed comparisons, we will see that on one hand Hybrid-IA finds slightly lower modularity values than Louvain, but outperforms all other metaheuristics, while on the other hand, it can detect communities more similar to the real ones when compared to those detected by Louvain.

Exploration of the optimal modularity in assembly line design

It is widely accepted that a proper structural modularity degree of assembly processes in terms of mass customization has a positive effect on their efficiency because it, among other things, increases manufacturing flexibility and productivity. On the other hand, most practical approaches to identify such a degree is rather based on intuition or analytical reasoning than on scientific foundations. However, the first way can be used for simple assembly tasks, but in more complex assembly processes, this method lags behind the second. The purpose was to create a methodology for selection of optimal modular assembly model from among a predefined set of alternatives. The methodology is based on exploration of the relations between modularity measures and complexity issues as well as the relationship between structural modularity and symmetry. Especially, the linkage between modularity and complexity properties has been explored in order to show how modularization can affect distribution of the total structural complexity across the entire assembly line. To solve this selection problem, three different methods are preliminary suggested and compared via a series of numerical tests. The two of them present the novel contribution of this work, while the third method developed earlier for the purpose of finding and evaluating community structure in networks was adapted for a given application domain. Based on obtained results, one of these method is prioritized over another, since it offers more promising results and precision too.

Role extraction for digraphs via neighborhood pattern similarity

We analyze the recovery of different roles in a network modeled by a directed graph, based on the so-called Neighborhood Pattern Similarity approach. Our analysis uses results from random matrix theory to show that, when assuming that the graph is generated as a particular stochastic block model with Bernoulli probability distributions for the different blocks, then the recovery is asymptotically correct when the graph has a sufficiently large dimension. Under these assumptions there is a sufficient gap between the dominant and dominated eigenvalues of the similarity matrix, which guarantees the asymptotic correct identification of the number of different roles. We also comment on the connections with the literature on stochastic block models, including the case of probabilities of order log(n)/n where n is the graph size. We provide numerical experiments to assess the effectiveness of the method when applied to practical networks of finite size.

A Hierarchical Random Graph Efficient Sampling Algorithm Based on Improved MCMC Algorithm

A hierarchical random graph (HRG) model combined with a maximum likelihood approach and a Markov Chain Monte Carlo algorithm can not only be used to quantitatively describe the hierarchical organization of many real networks, but also can predict missing connections in partly known networks with high accuracy. However, the computational cost is very large when hierarchical random graphs are sampled by the Markov Chain Monte Carlo algorithm (MCMC), so that the hierarchical random graphs, which can describe the characteristics of network structure, cannot be found in a reasonable time range. This seriously limits the practicability of the model. In order to overcome this defect, an improved MCMC algorithm called two-state transitions MCMC (TST-MCMC) for efficiently sampling hierarchical random graphs is proposed in this paper. On the Markov chain composed of all possible hierarchical random graphs, TST-MCMC can generate two candidate state variables during state transition and introduce a competition mechanism to filter out the worse of the two candidate state variables. In addition, the detailed balance of Markov chain can be ensured by using Metropolis–Hastings rule. By using this method, not only can the convergence speed of Markov chain be improved, but the convergence interval of Markov chain can be narrowed as well. Three example networks are employed to verify the performance of the proposed algorithm. Experimental results show that our algorithm is more feasible and more effective than the compared schemes.

A Graph-Cut-Based Approach to Community Detection in Networks

Networks can be used to model various aspects of our lives as well as relations among many real-world entities and objects. To detect a community structure in a network can enhance our understanding of the characteristics, properties, and inner workings of the network. Therefore, there has been significant research on detecting and evaluating community structures in networks. Many fields, including social sciences, biology, engineering, computer science, and applied mathematics, have developed various methods for analyzing and detecting community structures in networks. In this paper, a new community detection algorithm, which repeats the process of dividing a community into two smaller communities by finding a minimum cut, is proposed. The proposed algorithm is applied to some example network data and shows fairly good community detection results with comparable modularity Q values.

EC-BED-NETS: A Novel Deep Learning Framework for Recognizing Dominant Nodes in Multifaceted and Social Networks

Identification of influential nodes in multifaceted and social networks become one of the most significant researches in this booming digital world. Many strategies were proposed to determine the dominance of nodes based on their topographical information in the networks. Traditionally, centrality measurements were used directly on topographical structure of the networks and these measurements consider different characteristics related to structural and functional importance. The nonlinear link between the functional importance of the nodes, which makes the study so complicated and difficult to detect using traditional centrality measures. Inspired by the amazing execution structure of long short-term memory (LSTM), this article proposes the new hybrid boosted ensemble LSTM framework for solving the mentioned problem. This proposed framework adopts the enhanced centrality methods to construct the different feature vectors that can reflect the functional and structural location of the nodes in their networks, then categorizes the nodes in accordance with the measurements, and finally uses the proposed boosted deep learning framework to classify and rank the influential nodes. From the extensive experiments, the proposed framework has shown the best classification accuracy of 95.5% and it outperforms the other machine and deep learning models and even traditional centrality measurements.

Identification of robust retailing location patterns with complex network approaches

The problem of location is the cornerstone of strategic decisions in retail management. This decision is usually complex and multidimensional. One of the most relevant success factors is an adequate balanced tenancy, i.e., a complementary ecosystem of retail stores in the surroundings, both in planned and unplanned areas. In this paper, we use network theory to analyze the commercial spatial interactions in all the cities of Castile and Leon (an autonomous community in north-western Spain), Madrid, and Barcelona. Our approach encompasses different proposals both for the definition of the interaction networks and for their subsequent analyses. These methodologies can be used as pre-processing tools to capture features that formalize the relational dimension for location recommendation systems. Our results unveil the retail structure of different urban areas and enable a meaningful comparison between cities and methodologies. In addition, by means of consensus techniques, we identify a robust core of commercial relationships, independent of the particularities of each city, and thus help to distinguish transferable knowledge between cities. The results also suggest greater specialization of commercial space with city size.

LDPCD: A Novel Method for Locally Differentially Private Community Detection

As one of the cores of data analysis in large social networks, community detection has become a hot research topic in recent years. However, user's real social relationship may be at risk of privacy leakage and threatened by inference attacks because of the semitrusted server. As a result, community detection in social graphs under local differential privacy has gradually aroused the interest of industry and academia. On the one hand, the distortion of user's real data caused by existing privacy-preserving mechanisms can have a serious impact on the mining process of densely connected local graph structure, resulting in low utility of the final community division. On the other hand, private community detection requires to use the results of multiple user-server interactions to adjust user's partition, which inevitably leads to excessive allocation of privacy budget and large error of perturbed data. For these reasons, a new community detection method based on the local differential privacy model (named LDPCD) is proposed in this paper. Due to the introduction of truncated Laplace mechanism, the accuracy of user perturbation data is improved. In addition, the community divisive algorithm based on extremal optimization (EO) is also refined to reduce the number of interactions between users and the server. Thus, the total privacy overhead is reduced and strong privacy protection is guaranteed. Finally, LDPCD is applied in two commonly used real-world datasets, and its advantage is experimentally validated compared with two state-of-the-art methods.

Connecting the dots: The boons and banes of network modeling

Network modeling transforms data into a structure of nodes and edges such that edges represent relationships between pairs of objects, then extracts clusters of densely connected nodes in order to capture high-dimensional relationships hidden in the data. This efficient and flexible strategy holds potential for unveiling complex patterns concealed within massive datasets, but standard implementations overlook several key issues that can undermine research efforts. These issues range from data imputation and discretization to correlation metrics, clustering methods, and validation of results. Here, we enumerate these pitfalls and provide practical strategies for alleviating their negative effects. These guidelines increase prospects for future research endeavors as they reduce type I and type II (false-positive and false-negative) errors and are generally applicable for network modeling applications across diverse domains.

Cluster synchronization of networks via a canonical transformation for simultaneous block diagonalization of matrices

We study cluster synchronization of networks and propose a canonical transformation for simultaneous block diagonalization of matrices that we use to analyze the stability of the cluster synchronous solution. Our approach has several advantages as it allows us to: (1) decouple the stability problem into subproblems of minimal dimensionality while preserving physically meaningful information, (2) study stability of both orbital and equitable partitions of the network nodes, and (3) obtain a parameterization of the problem in a small number of parameters. For the last point, we show how the canonical transformation decouples the problem into blocks that preserve key physical properties of the original system. We also apply our proposed algorithm to analyze several real networks of interest, and we find that it runs faster than alternative algorithms from the literature.

Modularity in Biological Networks

Network modeling, from the ecological to the molecular scale has become an essential tool for studying the structure, dynamics and complex behavior of living systems. Graph representations of the relationships between biological components open up a wide variety of methods for discovering the mechanistic and functional properties of biological systems. Many biological networks are organized into a modular structure, so methods to discover such modules are essential if we are to understand the biological system as a whole. However, most of the methods used in biology to this end, have a limited applicability, as they are very specific to the system they were developed for. Conversely, from the statistical physics and network science perspective, graph modularity has been theoretically studied and several methods of a very general nature have been developed. It is our perspective that in particular for the modularity detection problem, biology and theoretical physics/network science are less connected than they should. The central goal of this review is to provide the necessary background and present the most applicable and pertinent methods for community detection in a way that motivates their further usage in biological research.

Network Analysis Based on Important Node Selection and Community Detection

The stability and robustness of a complex network can be significantly improved by determining important nodes and by analyzing their tendency to group into clusters. Several centrality measures for evaluating the importance of a node in a complex network exist in the literature, each one focusing on a different perspective. Community detection algorithms can be used to determine clusters of nodes based on the network structure. This paper shows by empirical means that node importance can be evaluated by a dual perspective—by combining the traditional centrality measures regarding the whole network as one unit, and by analyzing the node clusters yielded by community detection. Not only do these approaches offer overlapping results but also complementary information regarding the top important nodes. To confirm this mechanism, we performed experiments for synthetic and real-world networks and the results indicate the interesting relation between important nodes on community and network level.

Quantum inspired community detection for analysis of biodiversity change driven by land-use conversion and climate change

Community detection remains little explored in the analysis of biodiversity change. The challenges linked with global biodiversity change have also multiplied manifold in the past few decades. Moreover, most studies concerning biodiversity change lack the quantitative treatment central to species distribution modeling. Empirical analysis of species distribution and abundance is thus integral to the study of biodiversity loss and biodiversity alterations. Community detection is therefore expected to efficiently model the topological aspect of biodiversity change driven by land-use conversion and climate change; given that it has already proven superior for diverse problems in the domain of social network analysis and subgroup discovery in complex systems. Thus, quantum inspired community detection is proposed as a novel technique to predict biodiversity change considering tiger population in eighteen states of India; leading to benchmarking of two novel datasets. Elements of land-use conversion and climate change are explored to design these datasets viz.-Landscape based distribution and Number of tiger reserves based distribution respectively; for predicting regions expected to maximize Tiger population growth. Furthermore, validation of the proposed framework on the said datasets is performed using standard community detection metrics like-Modularity, Normalized Mutual Information (NMI), Adjusted Rand Index (ARI), Degree distribution, Degree centrality and Edge-betweenness centrality. Quantum inspired community detection has also been successful in demonstrating an association between biodiversity change, land-use conversion and climate change; validated statistically by Pearson's correlation coefficient and p value test. Finally, modularity distribution based on parameter tuning establishes the superiority of the second dataset based on the number of Tiger reserves-in predicting regions maximizing Tiger population growth fostering species distribution and abundance; apart from scripting a stronger correlation of biodiversity change with land-use conversion.

Comprehensive influence of topological location and neighbor information on identifying influential nodes in complex networks

Identifying the influential nodes of complex networks is now seen as essential for optimizing the network structure or efficiently disseminating information through networks. Most of the available methods determine the spreading capability of nodes based on their topological locations or the neighbor information, the degree of node is usually used to denote the neighbor information, and the k-shell is used to denote the locations of nodes, However, k-shell does not provide enough information about the topological connections and position information of the nodes. In this work, a new hybrid method is proposed to identify highly influential spreaders by not only considering the topological location of the node but also the neighbor information. The percentage of triangle structures is employed to measure both the connections among the neighbor nodes and the location of nodes, the contact distance is also taken into consideration to distinguish the interaction influence by different step neighbors. The comparison between our proposed method and some well-known centralities indicates that the proposed measure is more highly correlated with the real spreading process, Furthermore, another comprehensive experiment shows that the top nodes removed according to the proposed method are relatively quick to destroy the network than other compared semi-local measures. Our results may provide further insights into identifying influential individuals according to the structure of the networks.

Consistency landscape of network communities

The concept of community detection has long been used as a key device for handling the mesoscale structures in networks. Suitably conducted community detection reveals various embedded informative substructures of network topology. However, regarding the practical usage of community detection, it has always been a tricky problem to assign a reasonable community resolution for networks of interest. Because of the absence of the unanimously accepted criterion, most of the previous studies utilized rather ad hoc heuristics to decide the community resolution. In this work, we harness the concept of consistency in community structures of networks to provide the overall community resolution landscape of networks, which we eventually take to quantify the reliability of detected communities for a given resolution parameter. More precisely, we exploit the ambiguity in the results of stochastic detection algorithms and suggest a method that denotes the relative validity of community structures in regard to their stability of global and local inconsistency measures using multiple detection processes. Applying our framework to synthetic and real networks, we confirm that it effectively displays insightful fundamental aspects of community structures.

An ecological approach to structural flexibility in online communication systems

Human cognitive abilities are limited resources. Today, in the age of cheap information-cheap to produce, to manipulate, to disseminate-this cognitive bottleneck translates into hypercompetition for rewarding outcomes among actors. These incentives push actors to mutualistically interact with specific memes, seeking the virality of their messages. In turn, memes' chances to persist and spread are subject to changes in the communication environment. In spite of all this complexity, here we show that the underlying architecture of empirical actor-meme information ecosystems evolves into recurring emergent patterns. We then propose an ecology-inspired modelling framework, bringing to light the precise mechanisms causing the observed flexible structural reorganisation. The model predicts-and the data confirm-that users' struggle for visibility induces a re-equilibration of the network's mesoscale towards self-similar nested arrangements. Our final microscale insights suggest that flexibility at the structural level is not mirrored at the dynamical one.

Uncovering the Effect of pS202/pT205/pS208 Triple Phosphorylations on the Conformational Features of the Key Fragment G192-T212 of Tau Protein

Microtubule-associated protein tau is abnormally phosphorylated and forms the aggregates of paired helical filaments in Alzheimer's disease (AD) and other tauopathies. So far, the relationship and mechanism between the abnormal phosphorylation of tau and fibril formation is still unclear. Therefore, studying the effect of phosphorylation on the structure of tau protein is helpful to elucidate the pathogenic mechanism of tauopathies. It has been shown that pS202/pT205/pS208 triple phosphorylations located in the proline-rich region can promote tau aggregation. In this work, the effect of triple phosphorylations on tau structure was investigated by molecular dynamics simulations combined with multiple analytical methods of trajectories. The results showed that the conformational diversity of G192-T212 fragments decreased after phosphorylation compared with that of the wild-type. Moreover, the dynamic network and hydrogen bond analyses showed that the addition of pS208 phosphorylation can destroy the key hydrogen bonds and the network structure formed centered on pT205 at the C-terminal of the pS202/pT205 double phosphorylated peptide and then destroy the turn structure formed in the region of G207-R211. The destruction of this turn structure is considered to be the main reason for the aggregation of pS202/pT205/pS208 triple phosphorylations. For the pS202/pT205/pS208 triple phosphorylated system, the G207-R211 region is a coil structure, which is more extended and prone to aggregation. In a word, our results reveal the mechanism that pS202/pT205/pS208 triple phosphorylations promote tau aggregation at the atomic level, which can provide useful theoretical guidance for the rational design of effective therapeutic drugs against AD and other tauopathies.

Network analysis: An indispensable tool for curricula design. A real case-study of the degree on mathematics at the URJC in Spain

Content addition to courses and its subsequent correct sequencing in a study plan or curricula design context determine the success (and, in some cases, the failure) of such study plan in the acquisition of knowledge by students. In this work, we propose a decision model to guide curricular design committees in the tasks of course selection and sequencing in higher education contexts using a novel methodology based on network analysis. In this work, the local and global properties stemming from complex network analysis tools are studied in detail to facilitate the design of the study plan and to ensure its coherence by detecting the communities within a graph, and the local and global centrality of the courses and their dependencies are analyzed, as well as the overlapping subgroups and the functions and different positions among them. The proposed methodology is applied to the study of a real case at the Universidad Rey Juan Carlos.

Parallel label propagation algorithm based on weight and random walk

Community detection is a complex and meaningful process, which plays an important role in studying the characteristics of complex networks. In recent years, the discovery and analysis of community structures in complex networks has attracted the attention of many scholars, and many community discovery algorithms have been proposed. Many existing algorithms are only suitable for small-scale data, not for large-scale data, so it is necessary to establish a stable and efficient label propagation algorithm to deal with massive data and complex social networks. In this paper, we propose a novel label propagation algorithm, called WRWPLPA (Parallel Label Propagation Algorithm based on Weight and Random Walk). WRWPLPA proposes a new similarity calculation method combining weights and random walks. It uses weights and similarities to update labels in the process of label propagation, improving the accuracy and stability of community detection. First, weight is calculated by combining the neighborhood index and the position index, and the weight is used to distinguish the importance of the nodes in the network. Then, use random walk strategy to describe the similarity between nodes, and the label of nodes are updated by combining the weight and similarity. Finally, parallel propagation is comprehensively proposed to utilize label probability efficiently. Experiment results on artificial network datasets and real network datasets show that our algorithm has improved accuracy and stability compared with other label propagation algorithms.

Gumbel-softmax-based optimization: a simple general framework for optimization problems on graphs

In computer science, there exist a large number of optimization problems defined on graphs, that is to find a best node state configuration or a network structure, such that the designed objective function is optimized under some constraints. However, these problems are notorious for their hardness to solve, because most of them are NP-hard or NP-complete. Although traditional general methods such as simulated annealing (SA), genetic algorithms (GA), and so forth have been devised to these hard problems, their accuracy and time consumption are not satisfying in practice. In this work, we proposed a simple, fast, and general algorithm framework based on advanced automatic differentiation technique empowered by deep learning frameworks. By introducing Gumbel-softmax technique, we can optimize the objective function directly by gradient descent algorithm regardless of the discrete nature of variables. We also introduce evolution strategy to parallel version of our algorithm. We test our algorithm on four representative optimization problems on graph including modularity optimization from network science, Sherrington–Kirkpatrick (SK) model from statistical physics, maximum independent set (MIS) and minimum vertex cover (MVC) problem from combinatorial optimization on graph, and Influence Maximization problem from computational social science. High-quality solutions can be obtained with much less time-consuming compared to the traditional approaches.

Insights from graph theory on the morphologies of actomyosin networks with multilinkers

Quantifying the influence of microscopic details on the dynamics of development of the overall structure of a filamentous network is important in a number of biologically relevant contexts, but it is not obvious what order parameters can be used to adequately describe this complex process. In this paper we investigated the role of multivalent actin-binding proteins (ABPs) in reorganizing actin filaments into higher-order complex networks via a computer model of semiflexible filaments. We characterize the importance of local connectivity among actin filaments, as well as the global features of actomyosin networks. We first map the networks into local graph representations and then, using principles from network-theory order parameters, combine properties from these representations to gain insight into the heterogeneous morphologies of actomyosin networks at a global level. We find that ABPs with a valency greater than 2 promote filament bundles and large filament clusters to a much greater extent than bivalent multilinkers. We also show that active myosinlike motor proteins promote the formation of dendritic branches from a stalk of actin bundles. Our work motivates future studies to embrace network theory as a tool to characterize complex morphologies of actomyosin detected by experiments, leading to a quantitative understanding of the role of ABPs in manipulating the self-assembly of actin filaments into unique architectures that underlie the structural scaffold of a cell relating to its mobility and shape.

Age-Associated Differences of Modules and Hubs in Brain Functional Networks

Healthy aging is usually accompanied by changes in the functional modular organization of the human brain, which may result in the decline of cognition and underlying brain dysfunction. However, the relationship between age-related brain functional modular structure differences and cognition remain debatable. In this study, we investigated the age-associated differences of modules and hubs from young, middle and old age groups, using resting-state fMRI data from a large cross-sectional adulthood sample. We first divided the subjects into three age groups and constructed an individual-level network for each subject. Subsequently, a module-guided group-level network construction method was applied to form a weighted network for each group from which functional modules were detected. The intra- and inter-modular connectivities were observed negatively correlated with age. According to the detected modules, we found the number of connector hubs in the young group was more than middle-age and old group, while the quantity of provincial hubs in middle-age group was discovered more than other two groups. Further ROI-wise analysis shows that different hubs have distinct age-associated trajectories of intra- and inter-modular connections, which suggests the different types of topological role transitions in functional networks across age groups. Our results indicated an inverse association between functional segregation/integration with age, which demonstrated age-associated differences in communication effeciency. This study provides a new perspective and useful information to better understand the normal aging of brain networks.

Community Detection Using Restrained Random-Walk Similarity

In this paper, we propose a restrained random-walk similarity method for detecting the community structures of graphs. The basic premise of our method is that the starting vertices of finite-length random walks are judged to be in the same community if the walkers pass similar sets of vertices. This idea is based on our consideration that a random walker tends to move in the community including the walker's starting vertex for some time after starting the walk. Therefore, the sets of vertices passed by random walkers starting from vertices in the same community must be similar. The idea is reinforced with two conditions. First, we exclude abnormal random walks. Random walks that depart from each vertex are executed many times, and vertices that are rarely passed by the walkers are excluded from the set of vertices that the walkers may pass. Second, we forcibly restrain random walks to an appropriate length. In our method, a random walk is terminated when the walker repeatedly visits vertices that they have already passed. Experiments on real-world networks demonstrate that our method outperforms previous techniques in terms of accuracy.

MONET: a toolbox integrating top-performing methods for network modularization

SUMMARY

We define a disease module as a partition of a molecular network whose components are jointly associated with one or several diseases or risk factors thereof. Identification of such modules, across different types of networks, has great potential for elucidating disease mechanisms and establishing new powerful biomarkers. To this end, we launched the 'Disease Module Identification (DMI) DREAM Challenge', a community effort to build and evaluate unsupervised molecular network modularization algorithms. Here, we present MONET, a toolbox providing easy and unified access to the three top-performing methods from the DMI DREAM Challenge for the bioinformatics community.

AVAILABILITY AND IMPLEMENTATION

MONET is a command line tool for Linux, based on Docker and Singularity containers; the core algorithms were written in R, Python, Ada and C++. It is freely available for download at https://github.com/BergmannLab/MONET.git.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Path-based extensions of local link prediction methods for complex networks

Link prediction in a complex network is a problem of fundamental interest in network science and has attracted increasing attention in recent years. It aims to predict missing (or future) links between two entities in a complex system that are not already connected. Among existing methods, local similarity indices are most popular that take into account the information of common neighbours to estimate the likelihood of existence of a connection between two nodes. In this paper, we propose global and quasi-local extensions of some commonly used local similarity indices. We have performed extensive numerical simulations on publicly available datasets from diverse domains demonstrating that the proposed extensions not only give superior performance, when compared to their respective local indices, but also outperform some of the current, state-of-the-art, local and global link-prediction methods.