Showing papers on "Degree distribution published in 2012"
TL;DR: The social networks of the Hadza, a population of hunter-gatherers in Tanzania, are characterized, showing that Hadza networks have important properties also seen in modernized social networks, including a skewed degree distribution, degree assortativity, transitivity, reciprocity, geographic decay and homophily.
Abstract: Social networks show striking structural regularities, and both theory and evidence suggest that networks may have facilitated the development of large-scale cooperation in humans Here, we characterize the social networks of the Hadza, a population of hunter-gatherers in Tanzania We show that Hadza networks have important properties also seen in modernized social networks, including a skewed degree distribution, degree assortativity, transitivity, reciprocity, geographic decay and homophily We demonstrate that Hadza camps exhibit high between-group and low within-group variation in public goods game donations Network ties are also more likely between people who give the same amount, and the similarity in cooperative behaviour extends up to two degrees of separation Social distance appears to be as important as genetic relatedness and physical proximity in explaining assortativity in cooperation Our results suggest that certain elements of social network structure may have been present at an early point in human history Also, early humans may have formed ties with both kin and non-kin, based in part on their tendency to cooperate Social networks may thus have contributed to the emergence of cooperation
566 citations
TL;DR: A study of the controllability of network edge dynamics reveals that it differs from that of nodal dynamics, and that real-world networks are easier to control than their random counterparts.
Abstract: Surprisingly little is known about how network dynamics might be controlled, despite extensive research into how they behave. A study of the controllability of network edge dynamics reveals that it differs from that of nodal dynamics, and that real-world networks are easier to control than their random counterparts.
424 citations
TL;DR: The main conclusion of this article is that correlation can and should be used to measure connectivity, however appropriate null networks should beUsed to benchmark network measures in correlation networks, which are inherently more clustered than random networks.
404 citations
TL;DR: In this paper, the authors introduced the concept of control centrality to quantify the ability of a single node to control a directed weighted network and showed that it is mainly determined by the network's degree distribution.
Abstract: We introduce the concept of control centrality to quantify the ability of a single node to control a directed weighted network. We calculate the distribution of control centrality for several real networks and find that it is mainly determined by the network’s degree distribution. We show that in a directed network without loops the control centrality of a node is uniquely determined by its layer index or topological position in the underlying hierarchical structure of the network. Inspired by the deep relation between control centrality and hierarchical structure in a general directed network, we design an efficient attack strategy against the controllability of malicious networks.
292 citations
TL;DR: It is proved 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.
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.
269 citations
TL;DR: This work proposes a new method that describes the gray matter morphology of an individual cortex as a network, and demonstrates that intracortical similarities can be used to provide a robust statistical description of individualgray matter morphology.
Abstract: The characterization of gray matter morphology of individual brains is an important issue in neuroscience. Graph theory has been used to describe cortical morphology, with networks based on covariation of gray matter volume or thickness between cortical areas across people. Here, we extend this research by proposing a new method that describes the gray matter morphology of an individual cortex as a network. In these large-scale morphological networks, nodes represent small cortical regions, and edges connect regions that have a statistically similar structure. The method was applied to a healthy sample (n 5 14, scanned at 2 different time points). For all networks, we described the spatial degree distribution, average minimum path length, average clustering coefficient, small world property, and betweenness centrality (BC). Finally, we studied the reproducibility of all these properties. The networks showed more clustering than random networks and a similar minimum path length, indicating that they were ‘‘small world.’’ The spatial degree and BC distributions corresponded closely to those from groupderived networks. All network property values were reproducible over the 2 time points examined. Our results demonstrate that intracortical similarities can be used to provide a robust statistical description of individual gray matter morphology.
255 citations
Journal Article•
TL;DR: Inspired by the deep relation between control centrality and hierarchical structure in a general directed network, an efficient attack strategy is designed against the controllability of malicious networks.
Abstract: We introduce the concept of control centrality to quantify the ability of a single node to control a directed weighted network. We calculate the distribution of control centrality for several real networks and find that it is mainly determined by the network’s degree distribution. We show that in a directed network without loops the control centrality of a node is uniquely determined by its layer index or topological position in the underlying hierarchical structure of the network. Inspired by the deep relation between control centrality and hierarchical structure in a general directed network, we design an efficient attack strategy against the controllability of malicious networks.
235 citations
Posted Content•
TL;DR: It is shown that policies for regional resilience should focus on ex-ante regional diagnosis and targeted interventions on particular missing links, rather than ex-postmyopic applications of policies based on an unconditional increase of network relational density.
Abstract: This article develops an evolutionary framework of regional resilience with a primary focus on the structural properties of local knowledge networks. After presenting the network-based rationales of growth and structuring of clusters, we analyze under which structural conditions a regional cluster can achieve short-run competitiveness without compromising long-run resilience capabilities. We show that the properties of degree distribution (the level of hierarchy) and degree correlation (the level of structural homophily) of regional knowledge networks should be studied to understand how clusters succeed in combining technological lock-in with regional lock-out. We propose simple statistical measures of cluster structuring to highlight these properties and discuss the results in a policy-oriented analysis. We conclude showing that policies for regional resilience should focus on ex-ante regional diagnosis and targeted interventions on particular missing links, rather than ex-postmyopic applications of policies based on an unconditional increase of network relational density.
210 citations
TL;DR: In this article, the authors proposed a general method of moments approach that can be used to fit a large class of probability models through empirical counts of certain patterns in a graph and established some general asymptotic properties of empirical graph moments and proved consistency of the estimates as the graph size grows for all ranges of the average degree.
Abstract: Probability models on graphs are becoming increasingly important in many applications, but statistical tools for fitting such models are not yet well developed Here we propose a general method of moments approach that can be used to fit a large class of probability models through empirical counts of certain patterns in a graph We establish some general asymptotic properties of empirical graph moments and prove consistency of the estimates as the graph size grows for all ranges of the average degree including $\Omega(1)$ Additional results are obtained for the important special case of degree distributions
195 citations
TL;DR: This work addresses complex network controllability from the perspective of the minimum dominating set (MDS) and shows that the more heterogeneous a network degree distribution is, the easier it is to control the entire system.
Abstract: The possibility of controlling and directing a complex system's behavior at will is rooted in its interconnectivity and can lead to significant advances in disparate fields, ranging from nationwide energy saving to therapies that involve multiple targets. In this work, we address complex network controllability from the perspective of the minimum dominating set (MDS). Our theoretical calculations, simulations using artificially generated networks as well as real-world network analyses show that the more heterogeneous a network degree distribution is, the easier it is to control the entire system. We demonstrate that relatively few nodes are needed to control the entire network if the power-law degree exponent is smaller than 2, whereas many nodes are required if it is larger than 2.
158 citations
TL;DR: In this article, the authors show that the mechanism responsible of spreading depends on the nature of the process, and that epidemics with a transient state are boosted by the innermost core and epidemics allowing a steady state present a dual scenario, where either the hub independently sustains activity and propagates it to the rest of the system, or, alternatively, the inner most network core collectively turns into the active state, maintaining it globally.
Abstract: In contrast to previous common wisdom that epidemic activity in heterogeneous networks is dominated by the hubs with the largest number of connections, recent research has pointed out the role that the innermost, dense core of the network plays in sustaining epidemic processes Here we show that the mechanism responsible of spreading depends on the nature of the process Epidemics with a transient state are boosted by the innermost core Contrarily, epidemics allowing a steady state present a dual scenario, where either the hub independently sustains activity and propagates it to the rest of the system, or, alternatively, the innermost network core collectively turns into the active state, maintaining it globally In uncorrelated networks the former mechanism dominates if the degree distribution decays with an exponent larger than 5/2, and the latter otherwise Topological correlations, rife in real networks, may perturb this picture, mixing the role of both mechanisms
TL;DR: It is demonstrated that the ash cloud was unexpectedly disruptive because it was spatially coherent rather than uniformly random and the combination of their geographical distribution and their network architectures jeopardises their inherent hazard tolerance.
Abstract: The 2010 eruption of the Eyjafjallajokull volcano had a devastating effect on the European air traffic network, preventing air travel throughout most of Europe for 6 days (Oroian in ProEnvironment 3:5–8, 2010). The severity of the disruption was surprising as previous research suggests that this type of network should be tolerant to random hazard (Albert et al. in Nature 406(6794):378–382, 2000; Strogatz in Nature 410(6825):268–276, 2001). The source of this hazard tolerance lies in the degree distribution of the network which, for many real-world networks, has been shown to follow a power law (Albert et al. in Nature 401(6749):130–131, 1999; Albert et al. in Nature 406(6794):378–382, 2000). In this paper, we demonstrate that the ash cloud was unexpectedly disruptive because it was spatially coherent rather than uniformly random. We analyse the spatial dependence in air traffic networks and demonstrate how the combination of their geographical distribution and their network architectures jeopardises their inherent hazard tolerance.
19 Sep 2012
TL;DR: The feasibility of graph processing on heterogeneous (i.e., including both CPUs and GPUs) platforms is demonstrated as a cost-effective approach towards addressing the graph processing challenges above.
Abstract: Large, real-world graphs are famously difficult to process efficiently. Not only they have a large memory footprint but most graph processing algorithms entail memory access patterns with poor locality, data-dependent parallelism, and a low compute-to-memory access ratio. Additionally, most real-world graphs have a low diameter and a highly heterogeneous node degree distribution. Partitioning these graphs and simultaneously achieve access locality and load-balancing is difficult if not impossible. This paper demonstrates the feasibility of graph processing on heterogeneous (i.e., including both CPUs and GPUs) platforms as a cost-effective approach towards addressing the graph processing challenges above. To this end, this work (i) presents and evaluates a performance model that estimates the achievable performance on heterogeneous platforms; (ii) introduces TOTEM - a processing engine based on the Bulk Synchronous Parallel (BSP) model that offers a convenient environment to simplify the implementation of graph algorithms on heterogeneous platforms; and, (iii) demonstrates TOTEM'S efficiency by implementing and evaluating two graph algorithms (PageRank and breadth-first search). TOTEM achieves speedups close to the model's prediction, and applies a number of optimizations that enable linear speedups with respect to the share of the graph offloaded for processing to accelerators.
TL;DR: In this paper, the authors considered an SIR epidemic model propagating on a Configuration Model network, where the degree distribution of the vertices is given and where the edges are randomly matched, and the evolution of the epidemic is summed up into three measure-valued equations that describe the degrees of the susceptible individuals and the number of edges from an infectious or removed individual to the set of susceptibles.
Abstract: We consider an SIR epidemic model propagating on a Configuration Model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemic is summed up into three measure-valued equations that describe the degrees of the susceptible individuals and the number of edges from an infectious or removed individual to the set of susceptibles. These three degree distributions are sufficient to describe the course of the disease. The limit in large population is investigated. As a corollary, this provides a rigorous proof of the equations obtained by Volz (2008).
TL;DR: The experimental results of susceptible-infectious-recovered (SIR) dynamics suggest that the proposed all-around distance can act as a more accurate, stable indicator of influential nodes.
Abstract: Identifying the most influential nodes in complex networks provides a strong basis for understanding spreading dynamics and ensuring more efficient spread of information. Due to the heterogeneous degree distribution, we observe that current centrality measures are correlated in their results of nodes ranking. This paper introduces the concept of all-around nodes, which act like all-around players with good performance in combined metrics. Then, an all-around distance is presented for quantifying the influence of nodes. The experimental results of susceptible-infectious-recovered (SIR) dynamics suggest that the proposed all-around distance can act as a more accurate, stable indicator of influential nodes.
TL;DR: The importance of spatial network structure to understanding metapopulation abundance is demonstrated, and under what circumstances information on network structure should be complemented with information on the species life-history traits to understand persistence in heterogeneous environments is determined.
TL;DR: This work proposes and analyzes an onionlike candidate for a nearly optimal structure against simultaneous random and targeted high degree node attacks and investigates in detail the robustness enhancement due to assortative degree-degree correlation.
Abstract: Recently, it was found by Schneider et al. [Proc. Natl. Acad. Sci. USA 108, 3838 (2011)], using simulations, that scale-free networks with ``onion structure'' are very robust against targeted high degree attacks. The onion structure is a network where nodes with almost the same degree are connected. Motivated by this work, we propose and analyze, based on analytical considerations, an onionlike candidate for a nearly optimal structure against simultaneous random and targeted high degree node attacks. The nearly optimal structure can be viewed as a set of hierarchically interconnected random regular graphs,the degrees and populations of whose nodes are specified by the degree distribution. This network structure exhibits an extremely assortative degree-degree correlation and has a close relationship to the ``onion structure.'' After deriving a set of exact expressions that enable us to calculate the critical percolation threshold and the giant component of a correlated network for an arbitrary type of node removal, we apply the theory to the cases of random scale-free networks that are highly vulnerable against targeted high degree node removal. Our results show that this vulnerability can be significantly reduced by implementing this onionlike type of degree-degree correlation without much undermining the almost complete robustness against random node removal. We also investigate in detail the robustness enhancement due to assortative degree-degree correlation by introducing a joint degree-degree probability matrix that interpolates between an uncorrelated network structure and the onionlike structure proposed here by tuning a single control parameter. The optimal values of the control parameter that maximize the robustness against simultaneous random and targeted attacks are also determined. Our analytical calculations are supported by numerical simulations.
TL;DR: In this article, the authors model network formation when heterogeneous nodes enter sequentially and form connections through both random meetings and network-based search, but with type-dependent biases, and they show that there is "long-run integration" whereby the composition of types in sufficiently old nodes' neighborhoods approaches the global type-distribution, provided that the networkbased search is unbiased.
TL;DR: The degree distribution of the magnitude point process is power-law?shaped and does not change significantly with the increase of the threshold from 1.9 to 3.5, with mean value 3.11?0.06 as mentioned in this paper.
Abstract: The seismicity of Italy between April 16, 2005 and December 31, 2010 is investigated by means of the visibility graph method. The degree distribution of the magnitude point process is power-law?shaped. The method does not seem to detect time-clustering structures in the magnitude point process. The degree distribution does not change significantly with the increase of the magnitude threshold from 1.9 to 3.5. The exponent of the degree distribution shows a certain stability vs. the threshold magnitude, ranging between 3.00 and 3.25, with mean value 3.11?0.06.
TL;DR: An algorithm for constructing simple graphs from a given joint degree distribution, and a Monte Carlo Markov chain method for sampling them, and it is shown that the state space of simple graphs with a fixed degree distribution is connected via endpoint switches.
Abstract: One of the most influential recent results in network analysis is that many natural networks exhibit a power-law or log-normal degree distribution. This has inspired numerous generative models that match this property. However, more recent work has shown that while these generative models do have the right degree distribution, they are not good models for real-life networks due to their differences on other important metrics like conductance. We believe this is, in part, because many of these real-world networks have very different joint degree distributions, that is, the probability that a randomly selected edge will be between nodes of degree k and l. Assortativity is a sufficient statistic of the joint degree distribution, and it has been previously noted that social networks tend to be assortative, while biological and technological networks tend to be disassortative.We suggest understanding the relationship between network structure and the joint degree distribution of graphs is an interesting avenue of further research. An important tool for such studies are algorithms that can generate random instances of graphs with the same joint degree distribution. This is the main topic of this article, and we study the problem from both a theoretical and practical perspective. We provide an algorithm for constructing simple graphs from a given joint degree distribution, and a Monte Carlo Markov chain method for sampling them. We also show that the state space of simple graphs with a fixed degree distribution is connected via endpoint switches. We empirically evaluate the mixing time of this Markov chain by using experiments based on the autocorrelation of each edge. These experiments show that our Markov chain mixes quickly on these real graphs, allowing for utilization of our techniques in practice.
TL;DR: The Chinese air route network (CARN) is found to be a geographical network possessing exponential degree distribution, low clustering coefficient, large shortest path length and exponential spatial distance distribution that is obviously different from that of the Chinese airport network (CAN).
Abstract: The air route network, which supports all the flight activities of the civil aviation, is the most fundamental infrastructure of air traffic management system. In this paper, we study the Chinese air route network (CARN) within the framework of complex networks. We find that CARN is a geographical network possessing exponential degree distribution, low clustering coefficient, large shortest path length and exponential spatial distance distribution that is obviously different from that of the Chinese airport network (CAN). Besides, via investigating the flight data from 2002 to 2010, we demonstrate that the topology structure of CARN is homogeneous, howbeit the distribution of flight flow on CARN is rather heterogeneous. In addition, the traffic on CARN keeps growing in an exponential form and the increasing speed of west China is remarkably larger than that of east China. Our work will be helpful to better understand Chinese air traffic systems.
15 Mar 2012
TL;DR: An improved visibility graph method is proposed, i.e., limited penetrable visibility graph, for establishing complex network from time series, and combination parameters of network degree distribution can be used to classify typical three phase flow patterns, e.g., oil-in-water bubble flow, bubble-slug transitional flow and slug flow.
Abstract: We propose an improved visibility graph method, i.e., limited penetrable visibility graph, for establishing complex network from time series. Through evaluating the degree distributions of three visibility algorithms(visibility graph, horizontal visibility graph, limited penetrable visibility graph), we find that the horizontal visibility graph cannot distinguish signals from periodic, fractal, and chaotic systems; for fractal signal, the degree distributions obtained from visibility graph and limited penetrable visibility both can be well fitted to a power-law(scale-free distribution), but the anti-noise ability is not good; for periodic and chaotic signals, the limited penetrable visibility graph shows better anti-noise ability than visibility graph. In this regard, we use the limited penetrable visibility graph to extract the network degree distribution parameters from conductance fluctuating signals measured from oil-gas-water three-phase flow test. The results indicate that combination parameters of network degree distribution can be used to classify typical three phase flow patterns, e.g., oil-in-water bubble flow, bubble-slug transitional flow and slug flow.
TL;DR: The proposed approach relies on sampling without replacement and is thus also applicable for large sample fractions, and results in good estimates for the mean degree and the clustering coefficient, which, moreover, are almost independent from the response rate.
TL;DR: In this article, the authors explored the inheritance of the visibility graph from the original time series and found that degree distributions of visibility graphs extracted from Pseudo Brownian Motion series obtained by the Frequency Domain algorithm exhibit exponential behaviors, in which the exponential exponent is a binomial function of the Hurst index inherited in the time series.
Abstract: The visibility graph approach and complex network theory provide a new insight into time series analysis. The inheritance of the visibility graph from the original time series was further explored in the paper. We found that degree distributions of visibility graphs extracted from Pseudo Brownian Motion series obtained by the Frequency Domain algorithm exhibit exponential behaviors, in which the exponential exponent is a binomial function of the Hurst index inherited in the time series. Our simulations presented that the quantitative relations between the Hurst indexes and the exponents of degree distribution function are different for different series and the visibility graph inherits some important features of the original time series. Further, we convert some quarterly macroeconomic series including the growth rates of value-added of three industry series and the growth rates of Gross Domestic Product series of China to graphs by the visibility algorithm and explore the topological properties of graphs associated from the four macroeconomic series, namely, the degree distribution and correlations, the clustering coefficient, the average path length, and community structure. Based on complex network analysis we find degree distributions of associated networks from the growth rates of value-added of three industry series are almost exponential and the degree distributions of associated networks from the growth rates of GDP series are scale free. We also discussed the assortativity and disassortativity of the four associated networks as they are related to the evolutionary process of the original macroeconomic series. All the constructed networks have “small-world” features. The community structures of associated networks suggest dynamic changes of the original macroeconomic series. We also detected the relationship among government policy changes, community structures of associated networks and macroeconomic dynamics. We find great influences of government policies in China on the changes of dynamics of GDP and the three industries adjustment. The work in our paper provides a new way to understand the dynamics of economic development.
TL;DR: A model-selection method based on unsupervised learning is implemented that correctly classifies synthetic graphs, is robust under perturbations of the graphs, and shows that graphlet counts are a good way of capturing network structure.
Abstract: Several network models have been proposed to explain the link structure observed in online social networks. This paper addresses the problem of choosing the model that best fits a given real-world network. We implement a model-selection method based on unsupervised learning. An alternating decision tree is trained using synthetic graphs generated according to each of the models under consideration. We use a broad array of features, with the aim of representing different structural aspects of the network. Features include the frequency counts of small subgraphs (graphlets) as well as features capturing the degree distribution and small-world property. Our method correctly classifies synthetic graphs, and is robust under perturbations of the graphs. We show that the graphlet counts alone are sufficient in separating the training data, indicating that graphlet counts are a good way of capturing network structure. We tested our approach on four Facebook graphs from various American universities. The models th...
TL;DR: In this paper, the authors define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees.
Abstract: We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and spatial clustering gives this model a range of interesting properties. Empirical degree distributions converge to a limit law, which can be a power law with any exponent $\tau>2$. The average clustering coefficient of the networks converges to a positive limit. Finally, a phase transition occurs in the global clustering coefficients and empirical distribution of edge lengths when the power-law exponent crosses the critical value $\tau=3$. Our main tool in the proof of these results is a general weak law of large numbers in the spirit of Penrose and Yukich.
01 Oct 2012
TL;DR: This work presents asynchronous distributed algorithms, based on ratio consensus, that can be used to accurately estimate the number of nodes in a multi-component system whose communication topology is described by a directed graph.
Abstract: Many properties of interest in graph structures are based on the nodes' average degree (i.e., the average number of edges incident to/from each node). In this work, we present asynchronous distributed algorithms, based on ratio consensus, that can be used to accurately estimate the number of nodes in a multi-component system whose communication topology is described by a directed graph. In addition, we describe an asynchronous distributed algorithm that allows each node to introduce or terminate links in order to reach a target average degree in the network. Such an approach can be useful in many realistic scenarios; for example, for the introduction and removal of renewable energy resources in a power network, while maintaining an average degree that fulfils some structural and dynamical properties and/or optimises some performance indicators of the network. The effectiveness of the proposed algorithms is demonstrated via illustrative examples.
TL;DR: In this article, the critical coupling of an explosive synchronization in scale-free networks with Kuramoto oscillators has been investigated and it has been verified that the equation obtained has an inverse dependence on the network average degree.
Abstract: An explosive synchronization can be observed in scale-free networks when Kuramoto oscillators have natural frequencies equal to their number of connections. The present paper reports on mean-field approximations to determine the critical coupling of such explosive synchronization. It has been verified that the equation obtained for the critical coupling has an inverse dependence on the network average degree. This expression differs from those whose frequency distributions are unimodal and even. In this case, the critical coupling depends on the ratio between the first and second statistical moments of the degree distribution. Numerical simulations were also conducted to verify our analytical results.
Posted Content•
TL;DR: This work initiates the rigorous study of random hyperbolic graphs and confirms rigorously that the degree sequence follows a power-law distribution with controllable exponent and that the clustering is nonvanishing.
Abstract: In the last decades, the study of models for large real-world networks has been a very popular and active area of research. A reasonable model should not only replicate all the structural properties that are observed in real world networks (for example, heavy tailed degree distributions, high clustering and small diameter), but it should also be amenable to mathematical analysis. There are plenty of models that succeed in the first task but are hard to analyze rigorously. On the other hand, a multitude of proposed models, like classical random graphs, can be studied mathematically, but fail in creating certain aspects that are observed in real-world networks.
Recently, Papadopoulos, Krioukov, Boguna and Vahdat [INFOCOM'10] introduced a random geometric graph model that is based on hyperbolic geometry. The authors argued empirically and by some preliminary mathematical analysis that the resulting graphs have many of the desired properties. Moreover, by computing explicitly a maximum likelihood fit of the Internet graph, they demonstrated impressively that this model is adequate for reproducing the structure of real graphs with high accuracy.
In this work we initiate the rigorous study of random hyperbolic graphs. We compute exact asymptotic expressions for the expected number of vertices of degree k for all k up to the maximum degree and provide small probabilities for large deviations. We also prove a constant lower bound for the clustering coefficient. In particular, our findings confirm rigorously that the degree sequence follows a power-law distribution with controllable exponent and that the clustering is nonvanishing.
TL;DR: This work focuses on some measurable quantities of word co-occurrence network of each book for authorship characterization and employs complex networks theory to tackle this disputed problem.
Abstract: Authorship analysis by means of textual features is an important task in linguistic studies. We employ complex networks theory to tackle this disputed problem. In this work, we focus on some measurable quantities of word co-occurrence network of each book for authorship characterization. Based on the network features, attribution probability is defined for authorship identification. Furthermore, two scaling exponents, q-parameter and α-exponent, are combined to classify personal writing style with acceptable high resolution power. The q-parameter, generally known as the nonextensivity measure, is calculated for degree distribution and the α-exponent comes from a power law relationship between number of links and number of nodes in the co-occurrence network constructed for different books written by each author. The applicability of the presented method is evaluated in an experiment with thirty six books of five Persian litterateurs. Our results show high accuracy rate in authorship attribution.