Search

We address the problem of recommending online communities on social media platforms using design science. Our method is grounded in network science and leverages the random surfer model of the web, small-world networks, strength of weak connections, and connectivity to analyze three types of large-scale networks. In doing so, we design features for structural hole assortativity and local clustering coefficient rank to capture both the diversity and evolution of user interests. We also extract general online community features such as size and overlap. Experiments conducted on a large dataset of 34,000 lists created and subscribed to by 1,600 active Twitter users over a six-month period showed that our network features outperform the general and content features in terms of recommending communities at the top position. In addition, a combination of general and network features generated the best results in the top position with a significant performance improvement over using only the content features. A combination of all three types of features gave the best results in the top-5 and top-10 positions while improving the quality of recommendations at every other position. Our work outperforms the latest work on community recommendations on social media platforms and has major implications for the design of online community recommenders.

The study and analysis of real-world social, communication, information and citation networks for understanding their structure and identifying interesting patterns have cultivated the need for designing generative models for such networks. A generative model generates an artificial but a realistic-looking network with the same characteristics as that of a real network under study. In this paper, we propose a new generative model for generating realistic networks. Our proposed model is a blend of three key ideas namely preferential attachment, associativity of social links and randomness in real networks. We present a framework that first tests these ideas separately and then blends them into a mixed model based on the idea that a real-world graph could be formed by a mixture of these concepts. Our model can be used for generating static as well as time evolving graphs and this feature distinguishes it from previous approaches. We compare our model with previous methods for generating graphs and show that it outperforms in several aspects. We compare our graphs with real-world graphs across many metrics such as degree, clustering coefficient and path length distributions, assortativity, eigenvector centrality and modularity. In addition, we give both qualitative and quantitative results for clarity.

Online Social Networks (OSNs) are largely popular. People interact daily on networks such as Facebook, Twitter, YouTube, Email, Messenger, WhatsApp, Google+, Quora, LiveJournal etc. and the types of interaction on these networks are different. The types of content that people share on these networks are also different. Each of the OSNs serves a different purpose, such as sharing multimedia, microblogging, serving as a Question and Answer forum etc. Moreover, the community structure of these networks is also different. However, currently, all OSNs are considered as scale-free network based on the power-law degree distribution nature of these networks. In this paper, the effect of network properties such as density, diameter, degree distribution, global clustering coefficient, local clustering coefficient, homophily, assortativity and other centrality measures such as power-law exponent, eigenvector centrality and closeness centrality on seven online social networks, namely, Facebook, Twitter, YouTube, Email, Google+, Epinions and Gowalla networks are studied. The differences and similarities in the empirical results are analyzed, and the OSNs are divided categories based on the observed differences and similarities in network properties and centrality measures.

Complex networks have become an increasingly relevant research topic in machine learning, with many learning systems in the literature successfully exploring complex network properties and measures. In data classification, the use of complex networks allows the detection of structural and topological patterns related, for example, to the formation pattern of the input data. Some measures of complex networks have already been used in this sense. However, a systematic study capable of characterizing such measures in the context of data classification is lacking in the literature. In this work, we evaluate comparatively the predictive performance of some measures. Specifically, eight complex network measures were selected from the literature, namely: assortativity, average local clustering coefficient, average degree, betweenness, average shortest path length, closeness, global clustering coefficient and eigenvector centrality. For our analyses, both artificial and real-world data sets were considered. The results show that measures such as average shortest path and assortativity, besides presenting high predictive capability, are also more robust to the variation of the network structure. In summary, this research paves a way to support other related works in selecting more appropriate complex network measures for data classification.

Advances in magnetic resonance imaging, particularly diffusion imaging, have allowed researchers to analyze brain connectivity. Identification of structural connectivity differences between patients with normal cognition, cognitive impairment, and dementia could lead to new biomarker discoveries that could improve dementia diagnostics. In our study, we analyzed 22 patients (11 control group patients, 11 dementia group patients) that underwent 3T MRI diffusion tensor imaging (DTI) scans and the Montreal Cognitive Assessment (MoCA) test. We reconstructed DTI images and used the Desikan–Killiany–Tourville cortical parcellation atlas. The connectivity matrix was calculated, and graph theoretical analysis was conducted using DSI Studio. We found statistically significant differences between groups in the graph density, network characteristic path length, small-worldness, global efficiency, and rich club organization. We did not find statistically significant differences between groups in the average clustering coefficient and the assortativity coefficient. These statistically significant graph theory measures could potentially be used as quantitative biomarkers in cognitive impairment and dementia diagnostics.

In recent years, seismic time series has been used to construct complex network models in order to describe the seismic complexity. The effect of the factor focal depth has been elided in some of these models. In this paper, we aim to construct a new complex network model for seismicity by considering depth factor from the earthquake catalog and investigate the statistical properties of the network. Since the networks have been proved to be scale-free and small-world properties, the new network models should be studied whether the properties have changed. The results show that the new network model by considering depth factor is still scale-free and small-world. However, it is found that its average degree is smaller than the original network. The clustering coefficient increases at the year including mainshocks. The assortativity coefficient, which demonstrates preferential attachment of nodes, is positive and shows consistent pattern when main shocks occur.

Motivation: Epistatic miniarrary profile (EMAP) studies have enabled the mapping of large-scale genetic interaction networks and generated large amounts of data in model organisms. It provides an incredible set of molecular tools and advanced technologies that should be efficiently understanding the relationship between the genotypes and phenotypes of individuals. However, the network information gained from EMAP cannot be fully exploited using the traditional statistical network models. Because the genetic network is always heterogeneous, for example, the network structure features for one subset of nodes are different from those of the left nodes. Exponential-family random graph models (ERGMs) are a family of statistical models, which provide a principled and flexible way to describe the structural features (e.g., the density, centrality, and assortativity) of an observed network. However, the single ERGM is not enough to capture this heterogeneity of networks. In this paper, we consider a mixture ERGM (MixtureEGRM) networks, which model a network with several communities, where each community is described by a single EGRM. Results: EM algorithm is a classical method to solve the mixture problem, however, it will be very slow when the data size is huge in the numerous applications. We adopt an efficient novel online graph clustering algorithm to classify the graph nodes and estimate the ERGM parameters for the MixtureERGM. In comparison studies, the MixtureERGM outperforms the role analysis for the network cluster in which the mixture of exponential-family random graph model is developed for many ego-network according to their roles. One genetic interaction network of yeast and two real social networks (provided as supplemental materials, which can be found on the Computer Society Digital Library at http://doi.ieeecomputersociety.org/10.1109/TCBB.2017.2743711) show the wide potential application of the MixtureERGM.

In this paper, we conduct a complex-network analysis of the Bitcoin network. In particular, we design a new sampling method namely random walk with flying-back (RWFB) to conduct effective data sampling. We then conduct a comprehensive analysis of the Bitcoin network in terms of the degree distribution, clustering coefficient, the shortest path length, the assortativity, and the rich-club coefficient. There are several important observations from the Bitcoin network, such as small- world phenomenon and non-rich-club effect. This work brings up an in-depth understanding of the current Bitcoin blockchain network and offers implications for future directions in malicious activity and fraud detection in cryptocurrency blockchain networks.

Natural products have been widely used in the treatment of type 2 diabetes (T2D). However, their mechanisms are often obscured due to multi‐components and multi‐targets. The authors constructed a pathway‐based protein–protein association (PPA) network for target proteins of 13 α‐glucosidase inhibitors (AGIs) identified from Scutellaria baicalensis Georgi (SBG), designed to explore the underlying mechanisms. This network contained 118 nodes and 1167 connections. An uneven degree distribution and small‐world property were observed, characterised by high clustering coefficient and short average path length. The PPA network had an inherent hierarchy as C(k)∼k−0.71. It also exhibited potential weak disassortative mixing pattern, coupled with a decreased function Knn (k) and negative value of assortativity coefficient. These properties indicated that a few nodes were crucial to the network. PGH2, GNAS, MAPK1, MAPK3, PRKCA, and MAOA were then identified as key targets with the highest degree values and centrality indices. Additionally, a core subnetwork showed that chrysin, 5,8,2′‐trihydroxy‐7‐methoxyflavone, and wogonin were the main active constituents of these AGIs, and that the serotonergic synapse pathway was the critical pathway for SBG against T2D. The application of a pathway‐based protein–protein association network provides a novel strategy to explore the mechanisms of natural products on complex diseases.

Background Migraine is a primary headache disorder that can be classified into an episodic (EM) and a chronic form (CM). Network analysis within the graph-theoretical framework based on connectivity patterns provides an approach to observe large-scale structural integrity. We test the hypothesis that migraineurs are characterized by a segregated network. Methods 19 healthy controls (HC), 17 EM patients and 12 CM patients were included. Cortical thickness and subcortical volumes were computed, and topology was analyzed using a graph theory analytical framework and network-based statistics. We further used support vector machines regression (SVR) to identify whether these network measures were able to predict clinical parameters. Results Network based statistics revealed significantly lower interregional connectivity strength between anatomical compartments including the fronto-temporal, parietal and visual areas in EM and CM when compared to HC. Higher assortativity was seen in both patients’ group, with higher modularity for CM and higher transitivity for EM compared to HC. For subcortical networks, higher assortativity and transitivity were observed for both patients’ group with higher modularity for CM. SVR revealed that network measures could robustly predict clinical parameters for migraineurs. Conclusion We found global network disruption for EM and CM indicated by highly segregated network in migraine patients compared to HC. Higher modularity but lower clustering coefficient in CM is suggestive of more segregation in this group compared to EM. The presence of a segregated network could be a sign of maladaptive reorganization of headache related brain circuits, leading to migraine attacks or secondary alterations to pain., The Journal of Headache and Pain, 22 (1), ISSN:1129-2377, ISSN:1129-2369

An important problem in modeling networks is how to generate a randomly sampled graph with given degrees. A popular model is the configuration model, a network with assigned degrees and random connections. The erased configuration model is obtained when self-loops and multiple edges in the configuration model are removed. We prove an upper bound for the number of such erased edges for regularly-varying degree distributions with infinite variance, and use this result to prove central limit theorems for Pearson's correlation coefficient and the clustering coefficient in the erased configuration model. Our results explain the structural correlations in the erased configuration model and show that removing edges leads to different scaling of the clustering coefficient. We then prove that for the rank-1 inhomogeneous random graph, another null model that creates scale-free simple networks, the results for Pearson's correlation coefficient as well as for the clustering coefficient are similar to the results for the erased configuration model., An important problem in modeling networks is how to generate a randomly sampled graph with given degrees. A popular model is the configuration model, a network with assigned degrees and random connections. The erased configuration model is obtained when self-loops and multiple edges in the configuration model are removed. We prove an upper bound for the number of such erased edges for regularly-varying degree distributions with infinite variance, and use this result to prove central limit theorems for Pearson’s correlation coefficient and the clustering coefficient in the erased configuration model. Our results explain the structural correlations in the erased configuration model and show that removing edges leads to different scaling of the clustering coefficient. We prove that for the rank-1 inhomogeneous random graph, another null model that creates scale-free simple networks, the results for Pearson’s correlation coefficient as well as for the clustering coefficient are similar to the results for the erased configuration model.

Human contact networks are important ways for the spread of infectious diseases, and it is of great significance to study the structure of human contact networks in the real world. In this paper, the human contact data in a research institute of a university is collected using video surveillance devices, and the corresponding human contact network is constructed. On this basis, the structural characteristics of the human contact network are analyzed at the micro and macro levels respectively, and compared with the ER random network, WS small-world network and BA scale-free network. The results show that the human contact network cannot be accurately described by the three commonly used ideal networks, but it still has some structural characteristics of each ideal network. The contact network has more similarities in structure with the WS small-world network, including large clustering coefficient, modularity and average shortest path length, at the same time, it has more hierarchies and weak assortativity. This study can provide experimental support for the construction of network models in epidemic spreading dynamics, and is of great significance for the study of mechanism and control measures of epidemic spreading in complex networks.

Recent research on Parkinson's disease (PD) has demonstrated the topological abnormalities of structural covariance networks (SCNs) using various morphometric features from structural magnetic resonance images (sMRI). However, the sulcal depth (SD)-based SCNs have not been investigated. In this study, we used SD to investigate the topological alterations of SCNs in 60 PD patients and 56 age- and gender-matched healthy controls (HC). SCNs were constructed by thresholding SD correlation matrices of 68 regions and analyzed using graph theoretical approaches. Compared with HC, PD patients showed increased normalized clustering coefficient and normalized path length, as well as a reorganization of degree-based and betweenness-based hubs (i.e., less frontal hubs). Moreover, the degree distribution analysis showed more high-degree nodes in PD patients. In addition, we also found the increased assortativity and reduced robustness under a random attack in PD patients compared to HC. Taken together, these findings indicated an abnormal topological organization of SD-based SCNs in PD patients, which may contribute in understanding the pathophysiology of PD at the network level.

In the past decade, the study of the dynamics of complex networks has been a focus of research. In particular, the controllability of complex networks based on the nodal dynamics has received strong attention. As a result, significant theories have been formulated in network control. Target control theory is one of the most important results among these theories. This theory addresses how to select as few input nodes as possible to control the chosen target nodes in a nodal linear dynamic system. However, the research on how to control the target edges in switchboard dynamics, which is a dynamical process defined on the edges, has been lacking. This shortcoming has motivated us to give an effective control scheme for the target edges. Here, we propose the k-travel algorithm to approximately calculate the minimum number of driven edges and driver nodes for a directed tree-like network. For general cases, we put forward a greedy algorithm TEC to approximately calculate the minimum number of driven edges and driver nodes. Analytic calculations show that networks with large assortativity coefficient as well as small average shortest path are efficient in random target edge control, and networks with small clustering coefficient are efficient in local target edge control.

Protein-protein interactions are crucial in many biological pathways and facilitate cellular function. Investigating these interactions as a graph of pairwise interactions can help to gain a systemic understanding of cellular processes. It is known, however, that proteins interact with each other not exclusively in pairs but also in polyadic interactions and they can form multiprotein complexes, which are stable interactions between multiple proteins. In this manuscript, we use hypergraphs to investigate multiprotein complex data. We investigate two random null models to test which hypergraph properties occur as a consequence of constraints, such as the size and the number of multiprotein complexes. We find that assortativity, the number of connected components, and clustering differ from the data to these null models. Our main finding is that projecting a hypergraph of polyadic interactions onto a graph of pairwise interactions leads to the identification of different proteins as hubs than the hyper-graph. We find in our data set that the hypergraph degree is a more accurate predictor for gene-essentiality than the degree in the pairwise graph. We find that analysing a hypergraph as pairwise graph drastically changes the distribution of the local clustering coefficient. Furthermore, using a pairwise interaction representing multiprotein complex data may lead to a spurious hierarchical structure, which is not observed in the hypergraph. Hence, we illustrate that hypergraphs can be more suitable than pairwise graphs for the analysis of multiprotein complex data.

In this paper, we study the topological properties of the global supply chain network in terms of its degree distribution, clustering coefficient, degree-degree correlation, bow-tie structure, and community structure to test the efficient supply chain propositions proposed by E. J.S. Hearnshaw et al. The global supply chain data in the year 2017 are constructed by collecting various company data from the web site of Standard & Poor’s Capital IQ platform. The in- and out-degree distributions are characterized by a power law of the form of γin = 2.42 and γout = 2.11. The clustering coefficient decays 〈 C ( k ) 〉 ∼ k - β k with an exponent βk = 0.46. The nodal degree-degree correlations 〈knn(k)〉 indicates the absence of assortativity. The bow-tie structure of giant weakly connected component (GWCC) reveals that the OUT component is the largest and consists 41.1% of all firms. The giant strong connected component (GSCC) is comprised of 16.4% of all firms. We observe that upstream or downstream firms are located a few steps away from the GSCC. Furthermore, we uncover the community structures of the network and characterize them according to their location and industry classification. We observe that the largest community consists of the consumer discretionary sector based mainly in the United States (US). These firms belong to the OUT component in the bow-tie structure of the global supply chain network. Finally, we confirm the validity of Hearnshaw et al.’s efficient supply chain propositions, namely Proposition S1 (short path length), Proposition S2 (power-law degree distribution), Proposition S3 (high clustering coefficient), Proposition S4 (“fit-gets-richer” growth mechanism), Proposition S5 (truncation of power-law degree distribution), and Proposition S7 (community structure with overlapping boundaries) regarding the global supply chain network. While the original propositions S1 just mentioned a short path length, we found the short path from the GSCC to IN and OUT by analyzing the bow-tie structure. Therefore, the short path length in the bow-tie structure is a conceptual addition to the original propositions of Hearnshaw.

Online social networks (OSN) are an increasingly powerful force for information diffusion and opinion sharing in society. Thus, understanding and modeling their structure and behavior is critical. Researchers need vast databases of self-contained, appropriately-sized OSN topologies in order to test and train new algorithms and models to solve problems related to these platforms. In this paper, we present a flexible, robust, and novel model for generating synthetic networks which closely resemble real OSN network systems (e.g., Facebook and Twitter) that include community structures. We also present an automated parameter tuner which can match the model’s output to a given OSN topology. The model can then be used as a data factory to generate testbeds of synthetic topologies which closely resemble the given sample. We compare our model, tuned to match two large real-world OSN network samples, with the Barabasi-Albert model and the Lancichinetti-Fortunato-Radicchi benchmark used as baselines. We find that output of our proposed generative model more closely matches the target topologies, than either model, on a variety of important metrics — including clustering coefficient, modularity, assortativity, and average path length. Our model also organically generates robust, realistic communities, with non-trivial inter- and intra-community structure.

A probabilistic generative network model with n nodes and m overlapping layers is obtained as a superposition of m mutually independent Bernoulli random graphs of varying size and strength. When n and m are large and of the same order of magnitude, the model admits a sparse limiting regime with a tunable power-law degree distribution and nonvanishing clustering coefficient. This article presents an asymptotic formula for the joint degree distribution of adjacent nodes. This yields a simple analytical formula for the model assortativity, and opens up ways to analyze rank correlation coefficients suitable for random graphs with heavy-tailed degree distributions.

Time series produced by an idealized macro-economic model are analyzed by means of conversion to complex networks by three different methods: the recursive graph method, the natural visibility graph method and the ordinal partition graph method. For several values of one of the model’s control parameters yielding both fully chaotic time-series and intermittent chaos very close to periodicity the corresponding complex networks are obtained for each conversion algorithm, and several network metrics are evaluated: average degree, number of nodes, connectivity ratio, characteristic path length, clustering coefficient, assortativity and local dimensionality. Moreover, multifractal analysis of the chaotic time series is performed which reveals the multifractal structure of the orbits in phase space for the chaotic time series. This multifractal structure is also depicted in the scale-free nature of the corresponding complex networks which agrees with literature results. Most metrics clearly distinguish between fully chaotic and intermittent time series. Some metrics have significantly different values for chaotic series obtained at different values of the control parameter revealing subtle differences in phase space structure and system dynamics. The average degree of the ordinal partition networks together with assortativity showed that complex network time series analysis captures the repetition of particular patterns in the original time series and particular temporal correlations that would not be easy or even possible to capture with traditional non-linear analysis methods. Finally, the Lyapunov exponent of the time series is shown to be linearly correlated with the average local dimensionality metric of the complex network obtained by the visibility graph method, a result that is reported for the first time.

Using the OECD-ICIO (2018) Database, this paper constructs an ASEAN+3 value-added trade network and calculates its topological features, including the network as a whole and degree centralities of nodes from 2005 to 2015. Among aggregate topological features, the biggest fluctuation is index of average degree with downward trend while the other four indicators of average geodesic distance, reciprocity correlation, average clustering coefficient and degree assortativity are stable. In addition, the values of degree assortativity have been negative. From the perspective of nodes centralities, Japan and China have been top two according to the results of out-degree centrality and out-closeness centrality of nodes while Malaysia, Singapore, Vietnam, and Thailand rank high on the indices of in-degree centrality and in-closeness centrality of nodes. Brunei Darussalam has been less involved in ASEAN+3 value-added trade network during the sample period. The hub countries such as Japan, China, Malaysia and Singapore need to advance the regional economic cooperation based on the advantages of countries and existing production network.

An important challenge in the field of exponential random graphs (ERGs) is the fitting of non-trivial ERGs on large graphs. By utilizing fast matrix block-approximation techniques, we propose an approximative framework to such non-trivial ERGs that result in dyadic independence (i.e., edge independent) distributions, while being able to meaningfully model both local information of the graph (e.g., degrees) as well as global information (e.g., clustering coefficient, assortativity, etc.) if desired. This allows one to efficiently generate random networks with similar properties as an observed network, and the models can be used for several downstream tasks such as link prediction. Our methods are scalable to sparse graphs consisting of millions of nodes. Empirical evaluation demonstrates competitiveness in terms of both speed and accuracy with state-of-the-art methods -- which are typically based on embedding the graph into some low-dimensional space -- for link prediction, showcasing the potential of a more direct and interpretable probabalistic model for this task., Comment: Accepted for DSAA 2020 conference

Emergence of synchronization is a remarkable collective phenomena between apparently independent agents in numerous multilevel and complex systems. The evidence of synchronization ranges from the elementary biological organisms to the most sophisticated human societies. In this paper, the problem of synchronization of nonlinearly coupled dynamical networks of Hindmarsh–Rose neurons with a sigmoidal coupling function is addressed. Sufficient condition for synchrony in terms of network structure is developed. A study on the basis of attraction of the complete synchronization is carried out for different structured networks. Also the phase synchronization of dynamical network of Hindmarsh–Rose neurons are studied. The impact of different structural properties of complex network on the phase synchronization are analyzed. The synchronization of Hindmarsh–Rose neurons are evaluated and compared on different structured network like random, regular, small-world, scale-free and modular networks. Interestingly, it was found that networks with high clustering coefficient and neutral degree mixing pattern promote better synchronization. Some chimera like state are also found in different structural networks. Further the effect of time delay dynamics on the synchronization of nonlinearly coupled network of Hindmarsh–Rose neurons are illustrated.

Emergence of cooperation in social dilemmas is an essential phenomena for the functioning of numerous multilevel and complex systems. The evidence of cooperation ranges from the elementary biological organisms to the most sophisticated human societies. Although emergence of cooperation is widely experienced, but its evolution is not well explained, since natural selection typically promotes selfish behaviours which are often not socially optimal. In this paper the coevolution of network structure and emergence of cooperation is studied in four classes of social dilemmas, representing the prisoner's dilemma, Hawk–Dove, snowdrift and coordination classes of games, in structured populations defined by weighted complex networks. The strength of interaction between two individuals is represented by network (edge) weight, which changes according to individuals’ preference through the evolutionary network dynamics. Using evolutionary dynamic network based simulations of the games model on randomly weighted complete networks, we present a detailed study of the evolution of dynamic complex network through the evolution of the structural properties of a network, such as clustering coefficient, assortativity coefficient, entropy of degree distribution, average strength of interaction and the promotion of cooperative behaviour in all four classes of games. The effect of changing the cost-to-benefit ratio on these network properties and evolution of cooperation is also reported.

We analyze how the structure of complex networks of non-identical oscillators influences synchronization in the context of the Kuramoto model. The complex network metrics assortativity and clustering coefficient are used in order to generate network topologies of Erdös-Rényi, Watts-Strogatz, and Barabási-Albert types that present high, intermediate, and low values of these metrics. We also employ the total dissonance metric for neighborhood similarity, which generalizes to networks the standard concept of dissonance between two non-identical coupled oscillators. Based on this quantifier and using an optimization algorithm, we generate Similar, Dissimilar, and Neutral natural frequency patterns, which correspond to small, large, and intermediate values of total dissonance, respectively. The emergency of synchronization is numerically studied by considering these three types of dissonance patterns along with the network topologies generated by high, intermediate, and low values of the metrics assortativity and clustering coefficient. We find that, in general, low values of these metrics appear to favor phase locking, especially for the Similar dissonance pattern.

This paper proposes a tractable model that allows us to analyze how agents' perception of relationships with others determines the structures of networks. In our model, agents are endowed with their own multidimensional characteristics and their payoffs depend on the social distance between them. We characterize the clustering coefficient and average path length in stable networks, and analyze how they are related to the way agents measure social distances. The model predicts the small-world properties under a class of social distance that violates the triangle inequality. Allowing for heterogeneity in link-formation costs, the model also accommodates other well documented empirical patterns of social networks such as skewed degree distributions, positive assortativity of degrees, and clustering-degree correlation.

Social systems are increasingly being modelled as complex networks, and the interactions and decision making of individuals in such systems can be modelled using game theory. Therefore, networked game theory can be effectively used to model social dynamics. Individuals can use pure or mixed strategies in their decision making, and recent research has shown that there is a connection between the topological placement of an individual within a social network and the best strategy they can choose to maximise their returns. Therefore, if certain individuals have a preference to employ a certain strategy, they can be swapped or moved around within the social network to more desirable topological locations where their chosen strategies will be more effective. To this end, it has been shown that to increase the overall public good, the cooperators should be placed at the hubs, and the defectors should be placed at the peripheral nodes. In this paper, we tackle a related question, which is the time (or number of swaps) it takes for individuals who are randomly placed within the network to move to optimal topological locations which ensure that the public utility satisfies a certain utility threshold. We show that this time depends on the topology of the social network, and we analyse this topological dependence in terms of topological metrics such as scale-free exponent, assortativity, clustering coefficient, and Shannon information content. We show that the higher the scale-free exponent, the quicker the public utility threshold can be reached by swapping individuals from an initial random allocation. On the other hand, we find that assortativity has negative correlation with the time it takes to reach the public utility threshold. We find also that in terms of the correlation between information content and the time it takes to reach a public utility threshold from a random initial assignment, there is a bifurcation: one class of networks show a positive correlation, while another shows a negative correlation. Our results highlight that by designing networks with appropriate topological properties, one can minimise the need for the movement of individuals within a network before a certain public good threshold is achieved. This result has obvious implications for defence strategies in particular.

We examine the structure of the percolating cluster (PC) formed by site percolation on a random clustered network (RCN) model. Using the generating functions, we formulate the clustering coefficient and assortative coefficient of the PC. We analytically and numerically show that the PC in the highly clustered networks is clustered even at the percolation threshold. The assortativity of the PC depends on the details of the RCN. The PC at the percolation threshold is disassortative when the numbers of edges and triangles of each node are assigned by Poisson distributions, but assortative when each node in an RCN has the same small number of edges, most of which form triangles. This result seemingly contradicts the disassortativity of fractal networks, although the renormalization scheme unveils the disassortative nature of a fractal PC., 15 pages, 10 figures

This paper presents a method to assess the state of convergence of Ant Colony Optimization algorithms (ACO) using network science metrics. ACO are inspired by the behavior of ants in nature, and it is commonly used to solve combinatorial optimization problems. Network Science allows studying the structure and the dynamics of networks. This area of study provides metrics used to extract global information from networks in a particular moment. This paper aims to show that two network science metrics, the Clustering coefficient and the Assortativity, can be adapted and used to assess the pheromone graph and extract information to identify the convergence state of the ACO. We analyze the convergence of the four variations of the ACO in the Traveling Salesman Problem (TSP). Based on the obtained results, we demonstrate that it is possible to evaluate the convergence of the ACO for the TSP based on the proposed metrics, especially the adapted clustering coefficient.

Aging is one of the challenging problem in biology and medicine. Exploring the underlying behind the topological network of aging process will be advantageous for human health. This study analyses the behavior or characteristics of aging through network approach. As the network in this study is dynamic, we are able to observe topological changes of network over time of the aging key players. Integration of static protein-protein interaction (PPI) network data with human brain gene expressions is an approach we used to construct dynamical network. Through the network measurements; Degree Centrality, Closeness Centrality, Betweenness Centrality, Local Clustering Coefficient and Local Assortativity, the behavior of age-related protein are observed topologically. In this paper, we focused on network topology in elder and senior age category as these categories reflect the important topological changes.

Graph theory analysis on resting state electroencephalographic rhythms disclosed topological properties of cerebral network. In Alzheimer's disease (AD) patients, this approach showed mixed results. Granger causality matrices were used as input to the graph theory allowing to estimate the strength and the direction of information transfer between electrode pairs. The number of edges (degree), the number of inward edges (in-degree), of outgoing edges (out-degree) were statistically compared among healthy controls, patients with mild cognitive impairment due to AD (AD-MCI) and AD patients with mild dementia (ADD) to evaluate if degree abnormality could involve low and/or high degree vertices, the so called hubs, in both prodromal and over dementia stage. Clustering coefficient and local efficiency were evaluated as measures of network segregation, path length and global efficiency as measures of integration, the assortativity coefficient as a measure of resilience. Degree, in-degree and out-degree values were lower in AD-MCI and ADD than the control group for non-hubs and hubs vertices. The number of edges was preserved for frontal electrodes, where patients' groups showed an additional hub in F3. Clustering coefficient was lower in ADD compared with AD-MCI in the right occipital electrode, and it was positively correlated with mini mental state examination. Local and global efficiency values were lower in patients' than control groups. Our results show that the topology of the network is altered in AD patients also in its prodromal stage, begins with the reduction of the number of edges and the loss of the local and global efficiency.

Properties of complex networks represent a powerful set of tools that can be used to study the complex behaviour of these systems of interconnections. They can vary from properties represented as simplistic metrics (number of edges and nodes) to properties that reflect complex information of the connection between entities part of the network (assortativity degree, density or clustering coefficient). Such a topological property that has valuable implications on the study of the networks dynamics are network motifs - patterns of interconnections found in real-world networks. Knowing that one of the biggest issue with network motifs discovery is its algorithmic NP-complete nature, this paper intends to present a method to detect if a network is prone or not to generate motifs by making use of its topological properties while training various classification models. This approach wants to serve as a time saving pre-processing step for the state-of-the-art solutions used to detect motifs in Complex networks.

Management of systemic risk in financial markets is traditionally associated with setting (higher) capital requirements for market participants. There are indications that while equity ratios have been increased massively since the financial crisis, systemic risk levels might not have lowered, but even increased. It has been shown that systemic risk is to a large extent related to the underlying network topology of financial exposures. A natural question arising is how much systemic risk can be eliminated by optimally rearranging these networks and without increasing capital requirements. Overlapping portfolios with minimized systemic risk which provide the same market functionality as empirical ones have been studied by [pichler2018]. Here we propose a similar method for direct exposure networks, and apply it to cross-sectional interbank loan networks, consisting of 10 quarterly observations of the Austrian interbank market. We show that the suggested framework rearranges the network topology, such that systemic risk is reduced by a factor of approximately 3.5, and leaves the relevant economic features of the optimized network and its agents unchanged. The presented optimization procedure is not intended to actually re-configure interbank markets, but to demonstrate the huge potential for systemic risk management through rearranging exposure networks, in contrast to increasing capital requirements that were shown to have only marginal effects on systemic risk [poledna2017]. Ways to actually incentivize a self-organized formation toward optimal network configurations were introduced in [thurner2013] and [poledna2016]. For regulatory policies concerning financial market stability the knowledge of minimal systemic risk for a given economic environment can serve as a benchmark for monitoring actual systemic risk in markets., Comment: 25 pages

In this paper, we propose a class of models for generating spatial versions of three classic networks: Erdos-Renyi (ER), Watts-Strogatz (WS), and Barabasi-Albert (BA). We assume that nodes have geographical coordinates, are uniformly distributed over an m × m Cartesian space, and long-distance connections are penalized. Our computational results show higher clustering coefficient, assortativity, and transitivity in all three spatial networks, and imperfect power law degree distribution in the BA network. Furthermore, we analyze a special case with geographically clustered coordinates, resembling real human communities, in which points are clustered over k centers. Comparison between the uniformly and geographically clustered versions of the proposed spatial networks show an increase in values of the clustering coefficient, assortativity, and transitivity, and a lognormal degree distribution for spatially clustered ER, taller degree distribution and higher average path length for spatially clustered WS, and higher clustering coefficient and transitivity for the spatially clustered BA networks.

Modeling coauthorship networks helps to understand the emergence and propagation of thoughts in academic society. A random geometric graph is proposed to model coauthorship networks, the connection mechanism of which expresses the effects of the academic influences and homophily of authors, and the collaborations between research teams. Our analysis reveals that the modeled networks have a range of features of empirical coauthorship networks, namely, the degree distribution made up of a mixture Poisson distribution with a power-law tail, clear community structure, small-world, high clustering, and degree assortativity. Moreover, the underlying formulae of the tail and forepart of the degree distribution, and the tail of the scaling relation between local clustering coefficient and degree are derived for the modeled networks, and are also applicable to the empirical networks.

Weibo is the Twitter counterpart in China that has attracted hundreds of millions of users. We crawled an almost complete Weibo user network that contains 222 million users and 27 billion links in 2013. This paper analyzes the structural properties of this network, and compares it with a Twitter user network. The topological properties we studied include the degree distributions, connected components, distance distributions, reciprocity, clustering coefficient, PageRank centrality, and degree assortativity. We find that Weibo users have a higher diversity index, higher Gini index, but a lower reciprocity and clustering coefficient for most of the nodes. A surprising observation is that the reciprocity of Weibo is only about a quarter of the reciprocity of the Twitter user network. We also show that Weibo adoption rate correlates with economic development positively, and Weibo network can be used to quantify the connections between provinces and regions in China. In particular, point-wise mutual information is shown to be accurate in quantifying the strength of connections. We developed an interactive analyzing software framework for this study, and released the data and code online.

Earthquake network is investigated by considering the volume resolution and the temporal causality. We perform the numerical computations for network metrics from seismic time series data taken in Japan. For our case, we mainly treat the feature of the topological properties via various statistical quantities such as the characteristic path length, the average clustering coefficient, the small-worldness, the cost efficiency, the global efficiency, the modularity, and the assortativity. The universal and irregular properties of statistical quantities in earthquake network do not find unambiguously, but it may be inferred that these topological properties improve by implementing the method and its technique from registered data of earthquake networks.

Many networks generated by nature have two generic properties: they are formed in the process of preferential attachment and they are scale-free. Considering these features, by interfering with mechanism of the preferential attachment, we propose a generalisation of the Barab&aacute, si&ndash, Albert model&mdash, the &rsquo, Fractional Preferential Attachment&rsquo, (FPA) scale-free network model&mdash, that generates networks with time-independent degree distributions p ( k ) &sim, k &minus, &gamma, with degree exponent 2 &lt, &le, 3 (where &gamma, = 3 corresponds to the typical value of the BA model). In the FPA model, the element controlling the network properties is the f parameter, where f &isin, ( 0 , 1 &rang, Depending on the different values of f parameter, we study the statistical properties of the numerically generated networks. We investigate the topological properties of FPA networks such as degree distribution, degree correlation (network assortativity), clustering coefficient, average node degree, network diameter, average shortest path length and features of fractality. We compare the obtained values with the results for various synthetic and real-world networks. It is found that, depending on f, the FPA model generates networks with parameters similar to the real-world networks. Furthermore, it is shown that f parameter has a significant impact on, among others, degree distribution and degree correlation of generated networks. Therefore, the FPA scale-free network model can be an interesting alternative to existing network models. In addition, it turns out that, regardless of the value of f, FPA networks are not fractal.

Cryptocurrency is a well-developed blockchain technology application that is currently a heated topic throughout the world. The public availability of transaction histories offers an opportunity to analyze and compare different cryptocurrencies. In this paper, we present a dynamic network analysis of three representative blockchain-based cryptocurrencies: Bitcoin, Ethereum, and Namecoin. By analyzing the accumulated network growth, we find that, unlike most other networks, these cryptocurrency networks do not always densify over time, and they are changing all the time with relatively low node and edge repetition ratios. Therefore, we then construct separate networks on a monthly basis, trace the changes of typical network characteristics (including degree distribution, degree assortativity, clustering coefficient, and the largest connected component) over time, and compare the three. We find that the degree distribution of these monthly transaction networks cannot be well fitted by the famous power-law distribution, at the same time, different currency still has different network properties, e.g., both Bitcoin and Ethereum networks are heavy-tailed with disassortative mixing, however, only the former can be treated as a small world. These network properties reflect the evolutionary characteristics and competitive power of these three cryptocurrencies and provide a foundation for future research.

Communities are virtually ubiquitous in real-world networks, and the statistic of modularity index Q is the classical measurement for community detection algorithms. However, the relationship between the modularity property and network multilever micro-scale structures is still not clear. In this paper, we study community detection results both in artificial and real-life complex networks by constructing different order null networks, and the results uncover that how micro-structures (such as degree distribution, assortativity and clustering coefficient) affect community properties. Meanwhile, we also propose two novel null networks (increasing or decreasing community structures) to verify the robustness of different community detection algorithms. Our results indicate that the modularity index Q is not a suitable statistic to measure the weak community property which is widely available in empirical networks. Our findings can not only be used to test the robustness of different community detection methods, but also be helpful to uncover the correlation of network structures between microcosmic and mesoscopic scales.

The use of magnetoencephalogram (MEG) signals in cognitive neuroscience research to investigate the functioning of the brain has increased over recent years. In this sensor space study, Granger Causality (GC) and Transfer entropy (TE) were applied to resting state MEGs from 220 healthy volunteers (aged 7–84) to characterise the possible changes in causality due to age and gender. Additionally, graph theory principles were used to evaluate different network components such as integration (global efficiency), segregation (clustering coefficient and modularity), centrality (betweenness), and resilience (strength and assortativity). Results showed that males had higher GC than females until mid-adulthood (~60 years). However, this gender difference was not observed using TE. Moreover, complex network analysis results of low global efficiency, high clustering coefficient, and low node strength, suggest that at rest, the brain topology resembled a network made up of loosely connected modules that had segregated and disassortative nodes with low resistance to change. Statistical analyses of results from both techniques, using pairwise t-test and two-way ANOVA, showed that age had a significant effect (p < 0.05) in all brain regions for both genders with significant gender differences being observed over the anterior, posterior, left lateral and right lateral regions of the brain. The results from this study could be used to develop a fingerprint of healthy ageing, which can potentially be used to assist with the identification of alterations to background brain activity due to pathology.