Assortative Networks Research Articles

Integrating epigenomic data and 3D genomic structure with a new measure of chromatin assortativity.

BackgroundNetwork analysis is a powerful way of modeling chromatin interactions. Assortativity is a network property used in social sciences to identify factors affecting how people establish social ties. We propose a new approach, using chromatin assortativity, to integrate the epigenomic landscape of a specific cell type with its chromatin interaction network and thus investigate which proteins or chromatin marks mediate genomic contacts.ResultsWe use high-resolution promoter capture Hi-C and Hi-Cap data as well as ChIA-PET data from mouse embryonic stem cells to investigate promoter-centered chromatin interaction networks and calculate the presence of specific epigenomic features in the chromatin fragments constituting the nodes of the network. We estimate the association of these features with the topology of four chromatin interaction networks and identify features localized in connected areas of the network. Polycomb group proteins and associated histone marks are the features with the highest chromatin assortativity in promoter-centered networks. We then ask which features distinguish contacts amongst promoters from contacts between promoters and other genomic elements. We observe higher chromatin assortativity of the actively elongating form of RNA polymerase 2 (RNAPII) compared with inactive forms only in interactions between promoters and other elements.ConclusionsContacts among promoters and between promoters and other elements have different characteristic epigenomic features. We identify a possible role for the elongating form of RNAPII in mediating interactions among promoters, enhancers, and transcribed gene bodies. Our approach facilitates the study of multiple genome-wide epigenomic profiles, considering network topology and allowing the comparison of chromatin interaction networks.Electronic supplementary materialThe online version of this article (doi:10.1186/s13059-016-1003-3) contains supplementary material, which is available to authorized users.

Neuron-Like Networks Between Ribosomal Proteins Within the Ribosome.

From brain to the World Wide Web, information-processing networks share common scale invariant properties. Here, we reveal the existence of neural-like networks at a molecular scale within the ribosome. We show that with their extensions, ribosomal proteins form complex assortative interaction networks through which they communicate through tiny interfaces. The analysis of the crystal structures of 50S eubacterial particles reveals that most of these interfaces involve key phylogenetically conserved residues. The systematic observation of interactions between basic and aromatic amino acids at the interfaces and along the extension provides new structural insights that may contribute to decipher the molecular mechanisms of signal transmission within or between the ribosomal proteins. Similar to neurons interacting through “molecular synapses”, ribosomal proteins form a network that suggest an analogy with a simple molecular brain in which the “sensory-proteins” innervate the functional ribosomal sites, while the “inter-proteins” interconnect them into circuits suitable to process the information flow that circulates during protein synthesis. It is likely that these circuits have evolved to coordinate both the complex macromolecular motions and the binding of the multiple factors during translation. This opens new perspectives on nanoscale information transfer and processing.

CD-Based Indices for Link Prediction in Complex Network.

Lots of similarity-based algorithms have been designed to deal with the problem of link prediction in the past decade. In order to improve prediction accuracy, a novel cosine similarity index CD based on distance between nodes and cosine value between vectors is proposed in this paper. Firstly, node coordinate matrix can be obtained by node distances which are different from distance matrix and row vectors of the matrix are regarded as coordinates of nodes. Then, cosine value between node coordinates is used as their similarity index. A local community density index LD is also proposed. Then, a series of CD-based indices include CD-LD-k, CD*LD-k, CD-k and CDI are presented and applied in ten real networks. Experimental results demonstrate the effectiveness of CD-based indices. The effects of network clustering coefficient and assortative coefficient on prediction accuracy of indices are analyzed. CD-LD-k and CD*LD-k can improve prediction accuracy without considering the assortative coefficient of network is negative or positive. According to analysis of relative precision of each method on each network, CD-LD-k and CD*LD-k indices have excellent average performance and robustness. CD and CD-k indices perform better on positive assortative networks than on negative assortative networks. For negative assortative networks, we improve and refine CD index, referred as CDI index, combining the advantages of CD index and evolutionary mechanism of the network model BA. Experimental results reveal that CDI index can increase prediction accuracy of CD on negative assortative networks.

Topological impact of constrained fracture growth

The topology of two discrete fracture network models is compared to investigate the impact of constrained fracture growth. In the Poissonian discrete fracture network model the fractures are assigned length, position and orientation independent of all other fractures, while in the mechanical discrete fracture network model the fractures grow and the growth can be limited by the presence of other fractures. The topology is found to be impacted by both the choice of model, as well as the choice of rules for the mechanical model. A significant difference is the degree mixing. In two dimensions the Poissonian model results in assortative networks, while the mechanical model results in disassortative networks. In three dimensions both models produce disassortative networks, but the disassortative mixing is strongest for the mechanical model.

Are opinion leaders important to spread information to cope with extreme droughts in (all) irrigation systems? A network analysis

We propose that the ability of opinion leaders of influencing ordinary farmers to adopt more sustainable practices in irrigation systems during extremely dry periods depends on the type of social network in which they are embedded. We show that in disassortative networks, where influent people link preferentially to relatively disconnected ones, e.g., in large gravity-fed irrigation systems, opinion leaders can be important to encourage the adoption of sustainable practices because they tend to present relatively high betweenness centrality scores, which indicates a greater ability to bridge clusters of otherwise disconnected people. In assortative networks, i.e., in networks in which people tend to connect to other similar individuals, on the other hand, it seems that the ability of leaders to influence other people is not directly related to their betweeenness centrality degree. We conclude than that betweenness centrality is a source of influence only in disassortative networks, that additionally present low clustering coefficients. This suggests that opinion leaders may be important to help bridge the informational gap between agencies and stakeholders in some, but not in all, irrigation systems, in order to pave the way for the adoption of measures to cope with extreme droughts, like the one Brazil is currently experiencing.

Time-dependent degree-degree correlations in epileptic brain networks: from assortative to dissortative mixing.

We investigate the long-term evolution of degree-degree correlations (assortativity) in functional brain networks from epilepsy patients. Functional networks are derived from continuous multi-day, multi-channel electroencephalographic data, which capture a wide range of physiological and pathophysiological activities. In contrast to previous studies which all reported functional brain networks to be assortative on average, even in case of various neurological and neurodegenerative disorders, we observe large fluctuations in time-resolved degree-degree correlations ranging from assortative to dissortative mixing. Moreover, in some patients these fluctuations exhibit some periodic temporal structure which can be attributed, to a large extent, to daily rhythms. Relevant aspects of the epileptic process, particularly possible pre-seizure alterations, contribute marginally to the observed long-term fluctuations. Our findings suggest that physiological and pathophysiological activity may modify functional brain networks in a different and process-specific way. We evaluate factors that possibly influence the long-term evolution of degree-degree correlations.

Disassortative mixing patterns of drug-using and sex networks on HIV risk behaviour among young drug users in Yunnan, China

ObjectivesThe dominant mode of HIV transmission in China has changed from injection drug use to sexual contact. The objectives of this study were to describe the disassortative and assortative mixing patterns of drug-using and sex networks among young drug users in China. Study designCross-sectional study. MethodsRespondent-driven sampling (RDS) was used to recruit young drug users in an egocentric network study in Yunnan, China. Egos were categorized as having disassortative mixing network patterns if they reported both sex and drug-using networks. Egos who only had a sex network (no drug-using network), or only a drug-using network (no sex network) were categorized as having assortative mixing network patterns. Multiple logistic regression was performed to analyze the relationships between disassortative patterns with risky sexual behaviour and drug-using practices. ResultsA total of 426 participants were recruited into the study. Two hundred forty-two egos reported disassortative mixing patterns and 139 egos had assortative patterns. The RDS-adjusted proportion of having a disassortative pattern was 53.2%. Participants with disassortative patterns were more likely to engage in HIV risk behaviour compared to those with assortative patterns. Specifically, drug users with disassortative patterns reported more multiple sex partners (31.4% vs 19.6%), concurrent partnerships (52.1% vs 39.0%), non-regular sex partners (12.0% vs 4.3%), and sex partners who were IDUs (24.9% vs 12.5%). Consistent condom use with regular or non-regular partners was low (between 18.9% and 47.2%) regardless of the mixing pattern. However, parenteral risk for HIV transmission was relatively low in both groups. ConclusionsThe transition of the HIV epidemic in China from injection drug use to sexual contact may be attributed to disassortative mixing in drug-use and sexual networks. HIV programs should consider disassortative mixing patterns when designing new behavioural interventions.

Preferential attachment in randomly grown networks

We reintroduce the model of Callaway et al. (2001) as a special case of a more general model for random network growth. Vertices are added to the graph at a rate of 1, while edges are introduced at rate δ. Rather than edges being introduced at random, we allow for a degree of preferential attachment with a linear attachment kernel, parametrised by m. The original model is recovered in the limit of no preferential attachment, m→∞. As expected, even weak preferential attachment introduces a power-law tail to the degree distribution. Additionally, this generalisation retains a great deal of the tractability of the original along with a surprising range of behaviour, although key mathematical features are modified for finite m. In particular, the critical edge density, δc which marks the onset of a giant network component is reduced with increasing tendency for preferential attachment. The positive degree–degree correlation introduced by the unbiased growth process is offset by the skewed degree distribution, reducing the network assortativity.

Second-order centrality correlation in scale-free networks

Scale-free networks in which the degree displays a power-law distribution can be classified into assortative, disassortative, and neutral networks according to their degree–degree correlation. The second-order centrality proposed in a distributed computation manner is quick-calculated and accurate to identify critical nodes. We explore the second-order centrality correlation (SOC) for each type of the scale-free networks. The SOC–SOC correlation in assortative network and neutral network behaves similarly to the degree–degree correlation, while it behaves an apparent difference in disassortative networks. Experiments show that the invulnerability of most of scale-free networks behaves similarly under the node removal ordering by SOC centrality and degree centrality, respectively. The netscience network and the Yeast network behave a little differently because they are native disconnecting networks.

Sovereign public debt crisis in Europe. A network analysis

In this paper we analyse the evolving network structure of the quarterly public debt-to-GDP ratio from 2000 to 2014. By applying tools and concepts coming from complex systems we study the effects of the global financial crisis over public debt network connections and communities. Two main results arise from this analysis: firstly, countries public debts tend to synchronize their evolution, increasing global connectivity in the network and dramatically decreasing the number of communities. Secondly, a disruption in previous structure is observed at the time of the shock, emerging a more centralized and less diversify network topological organization which might be more prone to suffer contagion effects. This last fact is evidenced by an increasing tendency in countries of similar level of public debt to be connected between them, which we have quantified by the network assortativity.

Effects of assortative mixing in the second-order Kuramoto model.

In this paper we analyze the second-order Kuramoto model in the presence of a positive correlation between the heterogeneity of the connections and the natural frequencies in scale-free networks. We numerically show that discontinuous transitions emerge not just in disassortative but also in strongly assortative networks, in contrast with the first-order model. We also find that the effect of assortativity on network synchronization can be compensated by adjusting the phase damping. Our results show that it is possible to control collective behavior of damped Kuramoto oscillators by tuning the network structure or by adjusting the dissipation related to the phases' movement.

Robustness of oscillatory behavior in correlated networks.

Understanding network robustness against failures of network units is useful for preventing large-scale breakdowns and damages in real-world networked systems. The tolerance of networked systems whose functions are maintained by collective dynamical behavior of the network units has recently been analyzed in the framework called dynamical robustness of complex networks. The effect of network structure on the dynamical robustness has been examined with various types of network topology, but the role of network assortativity, or degree–degree correlations, is still unclear. Here we study the dynamical robustness of correlated (assortative and disassortative) networks consisting of diffusively coupled oscillators. Numerical analyses for the correlated networks with Poisson and power-law degree distributions show that network assortativity enhances the dynamical robustness of the oscillator networks but the impact of network disassortativity depends on the detailed network connectivity. Furthermore, we theoretically analyze the dynamical robustness of correlated bimodal networks with two-peak degree distributions and show the positive impact of the network assortativity.

A new form of assortativity in online social networks

The term assortativity indicates the tendency, for a network node, to be directly connected to other nodes that are someway similar. In more technical terms, a given feature is assortative in a network if the probability that an arc exists between two nodes having this feature is greater than the probability that an arc exists between two generic nodes. The role of assortativity in real-world and online social networks has been largely investigated in the literature, in which, starting from degree assortativity, several forms of assortativity have been analyzed. When moving from a single-social-network to a multiple-social-network perspective, new specific traits can be studied, also under the assortativity magnifying glass. This is the case of membership overlap among networks (i.e., the fact that people belong to more online social networks) as expression of different traits of users׳ personality. In this paper, we deal with the above issue, by defining two different measures of membership overlap assortativity, called Loose and Constrained Inter-social-network Assortativity, respectively and by observing that in two of the most representative online social networks, namely Facebook and Twitter, membership overlap is assortative.

Volatility behavior of visibility graph EMD financial time series from Ising interacting system

A financial market dynamics model is developed and investigated by stochastic Ising system, where the Ising model is the most popular ferromagnetic model in statistical physics systems. Applying two graph based analysis and multiscale entropy method, we investigate and compare the statistical volatility behavior of return time series and the corresponding IMF series derived from the empirical mode decomposition (EMD) method. And the real stock market indices are considered to be comparatively studied with the simulation data of the proposed model. Further, we find that the degree distribution of visibility graph for the simulation series has the power law tails, and the assortative network exhibits the mixing pattern property. All these features are in agreement with the real market data, the research confirms that the financial model established by the Ising system is reasonable.

Assortativity in complex networks

Assortativity in complex networks

Incorporating Assortativity and Degree Dependence into Scalable Network Models

Due to the recent availability of large complex networks, considerable analysis has focused on understanding and characterizing the properties of these networks. Scalable generative graph models focus on modeling distributions of graphs that match real world network properties and scale to large datasets. Much work has focused on modeling networks with a power law degree distribution, clustering, and small diameter. In network analysis, the assortativity statistic is defined as the correlation between the degrees of linked nodes in the network. The assortativity measure can distinguish between types of networks---social networks commonly exhibit positive assortativity, in contrast to biological or technological networks that are typically disassortative. Despite this, little work has focused on scalable graph models that capture assortativity in networks. The contributions of our work are twofold. First, we prove that an unbounded number of pairs of networks exist with the same degree distribution and assortativity, yet different joint degree distributions. Thus, assortativity as a network measure cannot distinguish between graphs with complex (non-linear) dependence in their joint degree distributions. Motivated by this finding, we introduce a generative graph model that explicitly estimates and models the joint degree distribution. Our Binned Chung Lu method accurately captures both the joint degree distribution and assortativity, while still matching characteristics such as the degree distribution and clustering coefficients. Further, our method has subquadratic learning and sampling methods that enable scaling to large, real world networks. We evaluate performance compared to other scalable graph models on six real world networks, including a citation network with over 14 million edges.

Homophily and Influence: Pricing to Harness Word-of-Mouth on Social Networks

Large-scale social platforms have enabled marketers to obtain rich data on the structure of word-of-mouth (WOM) networks and the correlation of friends' preferences (network assortativity). We study how the similarity or difference of friends' reservation prices for a product should affect the optimal price and advertising levels for that product. To this end, we build an analytical model of informative advertising and pricing over a social network. Connections between consumers are added in a way that allows neighbors' preferences to be positively or negatively correlated, thereby introducing homophily or heterophily in the model. Consumers may learn about products either directly via advertising, or via WOM spread by their peers who have adopted a product. We find that in the typical scenario when blanket advertising is not affordable, firms set a price lower than the naive optimum in order to leverage the social value of more price-sensitive customers. We also characterize the relationship between assortativity and the marketing instruments (price and advertising) of the firm, to find that either instrument may be substitutes or complements with assortativity depending on the niche or mainstream appeal of the product, the cost of advertising, the overall connectivity, and the assortativity of the network.

Assortative and disassortative mixing investigated using the spectra of graphs.

We investigate the impact of degree-degree correlations on the spectra of networks. Even though density distributions exhibit drastic changes depending on the (dis)assortative mixing and the network architecture, the short-range correlations in eigenvalues exhibit universal random matrix theory predictions. The long-range correlations turn out to be a measure of randomness in (dis)assortative networks. The analysis further provides insight into the origin of high degeneracy at the zero eigenvalue displayed by a majority of biological networks.

Information spreading in correlated microblog reposting network based on directed percolation theory

Due to the properties of rapidity, explosive, timeliness and complicated behavior for user, the research on information spreading progress and influence factors for microblog becomes a hot area of network public opinion. In this paper, firstly we use the contracting mapping principle to discuss the convergence conditions of the iterative algorithm. The numerical solution of the percolation threshold and the size of the largest out-component are proposed. Then the influence of assortativity is analyzed based on the generation model with varying parameter. The feasibility of the proposed algorithm is verified by collecting microblog reposting data. Experimental results demonstrate that four correlation characteristics are shown to have assortativity and disassortativity, but the results of message spreading are closer to that of the assortative network which is related to in-in and in-out degree correlation. It can be verified that the four types of correlation characteristics of a large part of nodes show their consistency for assortativity, through deleting a few nodes as well as extracting link scale for four degree correlations.

Evolutionary dynamics of the traveler's dilemma and minimum-effort coordination games on complex networks.

The traveler's dilemma game and the minimum-effort coordination game are social dilemmas that have received significant attention resulting from the fact that the predictions of classical game theory are inconsistent with the results found when the games are studied experimentally. Moreover, both the traveler's dilemma and the minimum-effort coordination games have potentially important applications in evolutionary biology. Interestingly, standard deterministic evolutionary game theory, as represented by the replicator dynamics in a well-mixed population, is also inadequate to account for the behavior observed in these games. Here we study the evolutionary dynamics of both these games in populations with interaction patterns described by a variety of complex network topologies. We investigate the evolutionary dynamics of these games through agent-based simulations on both model and empirical networks. In particular, we study the effects of network clustering and assortativity on the evolutionary dynamics of both games. In general, we show that the evolutionary behavior of the traveler's dilemma and minimum-effort coordination games on complex networks is in good agreement with that observed experimentally. Thus, formulating the traveler's dilemma and the minimum-effort coordination games on complex networks neatly resolves the paradoxical aspects of these games.