Showing papers on "Degree distribution published in 2013"

Pseudo-likelihood methods for community detection in large sparse networks

Abstract: Many algorithms have been proposed for fitting network models with communities, but most of them do not scale well to large networks, and often fail on sparse networks. Here we propose a new fast pseudo-likelihood method for fitting the stochastic block model for networks, as well as a variant that allows for an arbitrary degree distribution by conditioning on degrees. We show that the algorithms perform well under a range of settings, including on very sparse networks, and illustrate on the example of a network of political blogs. We also propose spectral clustering with perturbations, a method of independent interest, which works well on sparse networks where regular spectral clustering fails, and use it to provide an initial value for pseudo-likelihood. We prove that pseudo-likelihood provides consistent estimates of the communities under a mild condition on the starting value, for the case of a block model with two communities.

Growing Multiplex Networks

Abstract: We propose a modeling framework for growing multiplexes where a node can belong to different networks. We define new measures for multiplexes and we identify a number of relevant ingredients for modeling their evolution such as the coupling between the different layers and the distribution of node arrival times. The topology of the multiplex changes significantly in the different cases under consideration, with effects of the arrival time of nodes on the degree distribution, average shortest path length, and interdependence.

Nature of the Epidemic Threshold for the Susceptible-Infected-Susceptible Dynamics in Networks

Abstract: We develop an analytical approach to the susceptible-infected-susceptible epidemic model that allows us to unravel the true origin of the absence of an epidemic threshold in heterogeneous networks. We find that a delicate balance between the number of high degree nodes in the network and the topological distance between them dictates the existence or absence of such a threshold. In particular, small-world random networks with a degree distribution decaying slower than an exponential have a vanishing epidemic threshold in the thermodynamic limit.

Origins of power-law degree distribution in the heterogeneity of human activity in social networks

Abstract: The probability distribution of number of ties of an individual in a social network follows a scale-free power-law. However, how this distribution arises has not been conclusively demonstrated in direct analyses of people's actions in social networks. Here, we perform a causal inference analysis and find an underlying cause for this phenomenon. Our analysis indicates that heavy-tailed degree distribution is causally determined by similarly skewed distribution of human activity. Specifically, the degree of an individual is entirely random - following a “maximum entropy attachment” model - except for its mean value which depends deterministically on the volume of the users' activity. This relation cannot be explained by interactive models, like preferential attachment, since the observed actions are not likely to be caused by interactions with other people.

A novel link prediction algorithm for reconstructing protein–protein interaction networks by topological similarity

Abstract: Motivation: Recent advances in technology have dramatically increased the availability of protein–protein interaction (PPI) data and stimulated the development of many methods for improving the systems level understanding the cell. However, those efforts have been significantly hindered by the high level of noise, sparseness and highly skewed degree distribution of PPI networks. Here, we present a novel algorithm to reduce the noise present in PPI networks. The key idea of our algorithm is that two proteins sharing some higher-order topological similarities, measured by a novel random walk-based procedure, are likely interacting with each other and may belong to the same protein complex. Results: Applying our algorithm to a yeast PPI network, we found that the edges in the reconstructed network have higher biological relevance than in the original network, assessed by multiple types of information, including gene ontology, gene expression, essentiality, conservation between species and known protein complexes. Comparison with existing methods shows that the network reconstructed by our method has the highest quality. Using two independent graph clustering algorithms, we found that the reconstructed network has resulted in significantly improved prediction accuracy of protein complexes. Furthermore, our method is applicable to PPI networks obtained with different experimental systems, such as affinity purification, yeast two-hybrid (Y2H) and protein-fragment complementation assay (PCA), and evidence shows that the predicted edges are likely bona fide physical interactions. Finally, an application to a human PPI network increased the coverage of the network by at least 100%. Availability: www.cs.utsa.edu/~jruan/RWS/. Contact: Jianhua.Ruan@utsa.edu Supplementary information: Supplementary data are available at Bioinformatics online.

Multidimensional networks: foundations of structural analysis

Abstract: Complex networks have been receiving increasing attention by the scientific community, thanks also to the increasing availability of real-world network data. So far, network analysis has focused on the characterization and measurement of local and global properties of graphs, such as diameter, degree distribution, centrality, and so on. In the last years, the multidimensional nature of many real world networks has been pointed out, i.e. many networks containing multiple connections between any pair of nodes have been analyzed. Despite the importance of analyzing this kind of networks was recognized by previous works, a complete framework for multidimensional network analysis is still missing. Such a framework would enable the analysts to study different phenomena, that can be either the generalization to the multidimensional setting of what happens in monodimensional networks, or a new class of phenomena induced by the additional degree of complexity that multidimensionality provides in real networks. The aim of this paper is then to give the basis for multidimensional network analysis: we present a solid repertoire of basic concepts and analytical measures, which take into account the general structure of multidimensional networks. We tested our framework on different real world multidimensional networks, showing the validity and the meaningfulness of the measures introduced, that are able to extract important and non-random information about complex phenomena in such networks.

A Scalable Generative Graph Model with Community Structure

Abstract: Network data is ubiquitous and growing, yet we lack realistic generative network models that can be calibrated to match real-world data. The recently proposed Block Two-Level Erdss-Renyi (BTER) model can be tuned to capture two fundamental properties: degree distribution and clustering coefficients. The latter is particularly important for reproducing graphs with community structure, such as social networks. In this paper, we compare BTER to other scalable models and show that it gives a better fit to real data. We provide a scalable implementation that requires only O(d_max) storage where d_max is the maximum number of neighbors for a single node. The generator is trivially parallelizable, and we show results for a Hadoop MapReduce implementation for a modeling a real-world web graph with over 4.6 billion edges. We propose that the BTER model can be used as a graph generator for benchmarking purposes and provide idealized degree distributions and clustering coefficient profiles that can be tuned for user specifications.

A modified evidential methodology of identifying influential nodes in weighted networks

Abstract: How to identify influential nodes in complex networks is still an open hot issue. In the existing evidential centrality (EVC), node degree distribution in complex networks is not taken into consideration. In addition, the global structure information has also been neglected. In this paper, a new Evidential Semi-local Centrality (ESC) is proposed by modifying EVC in two aspects. Firstly, the Basic Probability Assignment (BPA) of degree generated by EVC is modified according to the actual degree distribution, rather than just following uniform distribution. BPA is the generation of probability in order to model uncertainty. Secondly, semi-local centrality combined with modified EVC is extended to be applied in weighted networks. Numerical examples are used to illustrate the efficiency of the proposed method.

Restreaming graph partitioning: simple versatile algorithms for advanced balancing

Abstract: Partitioning large graphs is difficult, especially when performed in the limited models of computation afforded to modern large scale computing systems. In this work we introduce restreaming graph partitioning and develop algorithms that scale similarly to streaming partitioning algorithms yet empirically perform as well as fully offline algorithms. In streaming partitioning, graphs are partitioned serially in a single pass. Restreaming partitioning is motivated by scenarios where approximately the same dataset is routinely streamed, making it possible to transform streaming partitioning algorithms into an iterative procedure. This combination of simplicity and powerful performance allows restreaming algorithms to be easily adapted to efficiently tackle more challenging partitioning objectives. In particular, we consider the problem of stratified graph partitioning, where each of many node attribute strata are balanced simultaneously. As such, stratified partitioning is well suited for the study of network effects on social networks, where it is desirable to isolate disjoint dense subgraphs with representative user demographics. To demonstrate, we partition a large social network such that each partition exhibits the same degree distribution in the original graph --- a novel achievement for non-regular graphs. As part of our results, we also observe a fundamental difference in the ease with which social graphs are partitioned when compared to web graphs. Namely, the modular structure of web graphs appears to motivate full offline optimization, whereas the locally dense structure of social graphs precludes significant gains from global manipulations.

Random walks on weighted networks.

Abstract: Random walks constitute a fundamental mechanism for a large set of dynamics taking place on networks. In this article, we study random walks on weighted networks with an arbitrary degree distribution, where the weight of an edge between two nodes has a tunable parameter. By using the spectral graph theory, we derive analytical expressions for the stationary distribution, mean first-passage time (MFPT), average trapping time (ATT), and lower bound of the ATT, which is defined as the average MFPT to a given node over every starting point chosen from the stationary distribution. All these results depend on the weight parameter, indicating a significant role of network weights on random walks. For the case of uncorrelated networks, we provide explicit formulas for the stationary distribution as well as ATT. Particularly, for uncorrelated scale-free networks, when the target is placed on a node with the highest degree, we show that ATT can display various scalings of network size, depending also on the same parameter. Our findings could pave a way to delicately controlling random-walk dynamics on complex networks.

Factors Determining Nestedness in Complex Networks

Abstract: Understanding the causes and effects of network structural features is a key task in deciphering complex systems. In this context, the property of network nestedness has aroused a fair amount of interest as regards ecological networks. Indeed, Bastolla et al. introduced a simple measure of network nestedness which opened the door to analytical understanding, allowing them to conclude that biodiversity is strongly enhanced in highly nested mutualistic networks. Here, we suggest a slightly refined version of such a measure of nestedness and study how it is influenced by the most basic structural properties of networks, such as degree distribution and degree-degree correlations (i.e. assortativity). We find that most of the empirically found nestedness stems from heterogeneity in the degree distribution. Once such an influence has been discounted - as a second factor - we find that nestedness is strongly correlated with disassortativity and hence - as random networks have been recently found to be naturally disassortative - they also tend to be naturally nested just as the result of chance.

Degree and clustering coefficient in sparse random intersection graphs

Abstract: We establish asymptotic vertex degree distribution and examine its relation to the clustering coecient in two popular random intersection graph models of Godehardt and Jaworski (2001). For sparse graphs with positive clustering coecient, we examine statistical dependence between the (local) clustering coecient and the degree. Our results are mathematically rigorous. They are consistent with the empirical observation of Foudalis et al. (2011) that \clustering correlates negatively with degree." Moreover, they explain empirical results on k 1 scaling of the local clustering coecient of a vertex of degree k reported in Ravasz and Barab asi (2003).

Kuramoto model with frequency-degree correlations on complex networks

Abstract: We study the Kuramoto model on complex networks, in which natural frequencies of phase oscillators and the vertex degrees are correlated. Using the annealed network approximation and numerical simulations, we explore a special case in which the natural frequencies of the oscillators and the vertex degrees are linearly coupled. We find that in uncorrelated scale-free networks with the degree distribution exponent $2l\ensuremath{\gamma}l3$, the model undergoes a first-order phase transition, while the transition becomes second order at $\ensuremath{\gamma}g3$. If $\ensuremath{\gamma}=3$, the phase synchronization emerges as a result of a hybrid phase transition that combines an abrupt emergence of synchronization, as in first-order phase transitions, and a critical singularity, as in second-order phase transitions. The critical fluctuations manifest themselves as avalanches in the synchronization process. Comparing our analytical calculations with numerical simulations for Erd\ifmmode \mbox{\H{o}}\else \H{o}\fi{}s-R\'enyi and scale-free networks, we demonstrate that the annealed network approach is accurate if the mean degree and size of the network are sufficiently large. We also study analytically and numerically the Kuramoto model on star graphs and find that if the natural frequency of the central oscillator is sufficiently large in comparison to the average frequency of its neighbors, then synchronization emerges as a result of a first-order phase transition. This shows that oscillators sitting at hubs in a network may generate a discontinuous synchronization transition.

s-core network decomposition: a generalization of k-core analysis to weighted networks.

Abstract: A broad range of systems spanning biology, technology, and social phenomena may be represented and analyzed as complex networks. Recent studies of such networks using $k$-core decomposition have uncovered groups of nodes that play important roles. Here, we present $s$-core analysis, a generalization of $k$-core (or $k$-shell) analysis to complex networks where the links have different strengths or weights. We demonstrate the $s$-core decomposition approach on two random networks (ER and configuration model with scale-free degree distribution) where the link weights are (i) random, (ii) correlated, and (iii) anticorrelated with the node degrees. Finally, we apply the $s$-core decomposition approach to the protein-interaction network of the yeast Saccharomyces cerevisiae in the context of two gene-expression experiments: oxidative stress in response to cumene hydroperoxide (CHP), and fermentation stress response (FSR). We find that the innermost $s$-cores are (i) different from innermost $k$-cores, (ii) different for the two stress conditions CHP and FSR, and (iii) enriched with proteins whose biological functions give insight into how yeast manages these specific stresses.

Detecting local community structures in complex networks based on local degree central nodes

Abstract: Detecting local communities in real-world graphs such as large social networks, web graphs, and biological networks has received a great deal of attention because obtaining complete information from a large network is still difficult and unrealistic nowadays. In this paper, we define the term local degree central node whose degree is greater than or equal to the degree of its neighbor nodes. A new method based on the local degree central node to detect the local community is proposed. In our method, the local community is not discovered from the given starting node, but from the local degree central node that is associated with the given starting node. Experiments show that the local central nodes are key nodes of communities in complex networks and the local communities detected by our method have high accuracy. Our algorithm can discover local communities accurately for more nodes and is an effective method to explore community structures of large networks.

Triadic closure dynamics drives scaling laws in social multiplex networks

Abstract: Social networks exhibit scaling laws for several structural characteristics, such as degree distribution, scaling of the attachment kernel and clustering coefficients as a function of node degree. A detailed understanding if and how these scaling laws are inter-related is missing so far, let alone whether they can be understood through a common, dynamical principle. We propose a simple model for stationary network formation and show that the three mentioned scaling relations follow as natural consequences of triadic closure. The validity of the model is tested on multiplex data from a well-studied massive multiplayer online game. We find that the three scaling exponents observed in the multiplex data for the friendship, communication and trading networks can simultaneously be explained by the model. These results suggest that triadic closure could be identified as one of the fundamental dynamical principles in social multiplex network formation.

Trace complexity of network inference

Abstract: The network inference problem consists of reconstructing the edge set of a network given traces representing the chronology of infection times as epidemics spread through the network. This problem is a paradigmatic representative of prediction tasks in machine learning that require deducing a latent structure from observed patterns of activity in a network, which often require an unrealistically large number of resources (e.g., amount of available data, or computational time). A fundamental question is to understand which properties we can predict with a reasonable degree of accuracy with the available resources, and which we cannot. We define the trace complexity as the number of distinct traces required to achieve high fidelity in reconstructing the topology of the unobserved network or, more generally, some of its properties. We give algorithms that are competitive with, while being simpler and more efficient than, existing network inference approaches. Moreover, we prove that our algorithms are nearly optimal, by proving an information-theoretic lower bound on the number of traces that an optimal inference algorithm requires for performing this task in the general case. Given these strong lower bounds, we turn our attention to special cases, such as trees and bounded-degree graphs, and to property recovery tasks, such as reconstructing the degree distribution without inferring the network. We show that these problems require a much smaller (and more realistic) number of traces, making them potentially solvable in practice.

Epidemic threshold and topological structure of susceptible-infectious-susceptible epidemics in adaptive networks.

Abstract: The interplay between disease dynamics on a network and the dynamics of the structure of that network characterizes many real-world systems of contacts. A continuous-time adaptive susceptible-infectious-susceptible (ASIS) model is introduced in order to investigate this interaction, where a susceptible node avoids infections by breaking its links to its infected neighbors while it enhances the connections with other susceptible nodes by creating links to them. When the initial topology of the network is a complete graph, an exact solution to the average metastable-state fraction of infected nodes is derived without resorting to any mean-field approximation. A linear scaling law of the epidemic threshold ?c as a function of the effective link-breaking rate ? is found. Furthermore, the bifurcation nature of the metastable fraction of infected nodes of the ASIS model is explained. The metastable-state topology shows high connectivity and low modularity in two regions of the ?,? plane for any effective infection rate ?>?c: (i) a “strongly adaptive” region with very high ? and (ii) a “weakly adaptive” region with very low ?. These two regions are separated from the other half-open elliptical-like regions of low connectivity and high modularity in a contour-line-like way. Our results indicate that the adaptation of the topology in response to disease dynamics suppresses the infection, while it promotes the network evolution towards a topology that exhibits assortative mixing, modularity, and a binomial-like degree distribution.

Degree Distribution in Quantum Walks on Complex Networks

Abstract: Google's search engine algorithmically determines the relative importance of the world's webpages by exploiting the physics of a classical random walker on the complex network of nodes (pages) and links (hyperlinks). What happens if the classical random walker is replaced by a quantum one? Researchers develop and investigate a simple model of a quantum walker on a complex network, uncovering interesting quantum-classical correspondence as well as fundamentally intriguing differences.

Triadic closure dynamics drives scaling-laws in social multiplex networks

Abstract: Social networks exhibit scaling-laws for several structural characteristics, such as the degree distribution, the scaling of the attachment kernel, and the clustering coefficients as a function of node degree. A detailed understanding if and how these scaling laws are inter-related is missing so far, let alone whether they can be understood through a common, dynamical principle. We propose a simple model for stationary network formation and show that the three mentioned scaling relations follow as natural consequences of triadic closure. The validity of the model is tested on multiplex data from a well studied massive multiplayer online game. We find that the three scaling exponents observed in the multiplex data for the friendship, communication and trading networks can simultaneously be explained by the model. These results suggest that triadic closure could be identified as one of the fundamental dynamical principles in social multiplex network formation.

Characterizing traffic time series based on complex network theory

Abstract: A complex network is a powerful tool to research complex systems, traffic flow being one of the most complex systems. In this paper, we use complex network theory to study traffic time series, which provide a new insight into traffic flow analysis. Firstly, the phase space, which describes the evolution of the behavior of a nonlinear system, is reconstructed using the delay embedding theorem. Secondly, in order to convert the new time series into a complex network, the critical threshold is estimated by the characteristics of a complex network, which include degree distribution, cumulative degree distribution, and density and clustering coefficients. We find that the degree distribution of associated complex network can be fitted with a Gaussian function, and the cumulative degree distribution can be fitted with an exponential function. Density and clustering coefficients are then researched to reflect the change of connections between nodes in complex network, and the results are in accordance with the observation of the plot of an adjacent matrix. Consequently, based on complex network analysis, the proper range of the critical threshold is determined. Finally, to mine the nodes with the closest relations in a complex network, the modularity is calculated with the increase of critical threshold and the community structure is detected according to the optimal modularity. The work in our paper provides a new way to understand the dynamics of traffic time series.

Topological properties of a time-integrated activity-driven network.

Abstract: Here we consider the topological properties of the integrated networks emerging from the activity-driven model [N. Perra et al., Sci. Rep. 2, 469 (2012)], a temporal network model recently proposed to explain the power-law degree distribution empirically observed in many real social networks. By means of a mapping to a hidden-variable network model, we provide analytical expressions for the main topological properties of the integrated network, depending on the integration time and the distribution of activity potential characterizing the model. The expressions obtained, exacts in some cases, the results of controlled asymptotic expansions in others, are confirmed by means of extensive numerical simulations. Our analytical approach, which highlights the differences of the model with respect to the empirical observations made in real social networks, can be easily extended to deal with improved, more realistic modifications of the activity-driven network paradigm.

Metastable densities for the contact process on power law random graphs

Abstract: We consider the contact process on a random graph with fixed degree distribution given by a power law. We follow the work of Chatterjee and Durrett (2009), who showed that for arbitrarily small infection parameter $\lambda$, the survival time of the process is larger than a stretched exponential function of the number of vertices, $n$. We obtain sharp bounds for the typical density of infected sites in the graph, as $\lambda$ is kept fixed and $n$ tends to infinity. We exhibit three different regimes for this density, depending on the tail of the degree law.

Large deviations of empirical neighborhood distribution in sparse random graphs

Abstract: Consider the Erdős-Renyi random graph on n vertices where each edge is present independently with probability c/n, with c>0 fixed. For large n, a typical random graph locally behaves like a Galton-Watson tree with Poisson offspring distribution with mean c. Here, we study large deviations from this typical behavior within the framework of the local weak convergence of finite graph sequences. The associated rate function is expressed in terms of an entropy functional on unimodular measures and takes finite values only at measures supported on trees. We also establish large deviations for other commonly studied random graph ensembles such as the uniform random graph with given number of edges growing linearly with the number of vertices, or the uniform random graph with given degree sequence. To prove our results, we introduce a new configuration model which allows one to sample uniform random graphs with a given neighborhood distribution, provided the latter is supported on trees. We also introduce a new class of unimodular random trees, which generalizes the usual Galton Watson tree with given degree distribution to the case of neighborhoods of arbitrary finite depth. These generalized Galton Watson trees turn out to be useful in the analysis of unimodular random trees and may be considered to be of interest in their own right.

Visibility graph network analysis of gold price time series

Abstract: Mapping time series into a visibility graph network, the characteristics of the gold price time series and return temporal series, and the mechanism underlying the gold price fluctuation have been explored from the perspective of complex network theory. The network degree distribution characters, which change from power law to exponent law when the series was shuffled from original sequence, and the average path length characters, which change from L ∼ ln N into ln L ∼ ln N as the sequence was shuffled, demonstrate that price series and return series are both long-rang dependent fractal series. The relations of Hurst exponent to the power-law exponent of degree distribution demonstrate that the logarithmic price series is a fractal Brownian series and the logarithmic return series is a fractal Gaussian series. Power-law exponents of degree distribution in a time window changing with window moving demonstrates that a logarithmic gold price series is a multifractal series. The Power-law average clustering coefficient demonstrates that the gold price visibility graph is a hierarchy network. The hierarchy character, in light of the correspondence of graph to price fluctuation, means that gold price fluctuation is a hierarchy structure, which appears to be in agreement with Elliot’s experiential Wave Theory on stock price fluctuation, and the local-rule growth theory of a hierarchy network means that the hierarchy structure of gold price fluctuation originates from persistent, short term factors, such as short term speculation.

Community detection in complex networks

Abstract: The stochastic block model is a powerful tool for inferring community structure from network topology. However, the simple block model considers community structure as the only underlying attribute for forming the relational interactions among the nodes, this makes it prefer a Poisson degree distribution within each community, while most real-world networks have a heavy-tailed degree distribution. This is essentially because the simple assumption under the traditional block model is not consistent with some real-world circumstances where factors other than the community memberships such as overall popularity also heavily affect the pattern of the relational interactions. The degree-corrected block model can accommodate arbitrary degree distributions within communities by taking nodes' popularity or degree into account. But since it takes the vertex degrees as parameters rather than generating them, it cannot use them to help it classify the vertices, and its natural generalization to directed graphs cannot even use the orientations of the edges. We developed several variants of the block model with the best of both worlds: they can use vertex degrees and edge orientations in the classification process, while tolerating heavy-tailed degree distributions within communities. We show that for some networks, including synthetic networks and networks of word adjacencies in English text, these new block models achieve a higher accuracy than either standard or degree-corrected block models. Another part of my work is to develop even more generalized block models, which incorporates other attributes of the nodes. Many data sets contain rich information about objects, as well as pairwise relations between them. For instance, in networks of websites, scientific papers, patents and other documents, each node has content consisting of a collection of words, as well as hyperlinks or citations to other nodes. In order to perform inference on such data sets, and make predictions and recommendations, it is useful to have models that are able to capture the processes which generate the text at each node as well as the links between them. Our work combines classic ideas in topic modeling with a variant of the mixed-membership block model recently developed in the statistical physics community. The resulting model has the advantage that its parameters, including the mixture of topics of each document and the resulting overlapping communities, can be inferred with a simple and scalable expectation-maximization algorithm. We test our model on three data sets, performing unsupervised topic classification and link prediction. For both tasks, our model outperforms several existing state-of-the-art methods, achieving higher accuracy with significantly less computation, analyzing a data set with 1.3 million words and 44 thousand links in a few minutes.

Complex Network Approach to the Statistical Features of the Sunspot Series

Abstract: Complex network approaches have been recently developed as an alternative framework to study the statistical features of time-series data. We perform a visibility-graph analysis on both the daily and monthly sunspot series. Based on the data, we propose two ways to construct the network: one is from the original observable measurements and the other is from a negative-inverse-transformed series. The degree distribution of the derived networks for the strong maxima has clear non-Gaussian properties, while the degree distribution for minima is bimodal. The long-term variation of the cycles is reflected by hubs in the network which span relatively large time intervals. Based on standard network structural measures, we propose to characterize the long-term correlations by waiting times between two subsequent events. The persistence range of the solar cycles has been identified over 15\,--\,1000 days by a power-law regime with scaling exponent $\gamma = 2.04$ of the occurrence time of the two subsequent and successive strong minima. In contrast, a persistent trend is not present in the maximal numbers, although maxima do have significant deviations from an exponential form. Our results suggest some new insights for evaluating existing models. The power-law regime suggested by the waiting times does indicate that there are some level of predictable patterns in the minima.

Model of complex networks based on citation dynamics

Abstract: Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. These include scale-free degree distributions, small-world structure and assortative mixing by degree, which are also the properties captured by different random graph models proposed in the literature. However, many (non-social) real-world networks are in fact disassortative by degree. Thus, we here propose a simple evolving model that generates networks with most common properties of real-world networks including degree disassortativity. Furthermore, the model has a natural interpretation for citation networks with different practical applications.