Showing papers in "Journal of Complex Networks in 2018"

Network analysis of particles and grains

Abstract: The arrangements of particles and forces in granular materials have a complex organization on multiple spatial scales that ranges from local structures to mesoscale and system-wide ones. This multiscale organization can affect how a material responds or reconfigures when exposed to external perturbations or loading. The theoretical study of particle-level, force-chain, domain, and bulk properties requires the development and application of appropriate physical, mathematical, statistical, and computational frameworks. Traditionally, granular materials have been investigated using particulate or continuum models, each of which tends to be implicitly agnostic to multiscale organization. Recently, tools from network science have emerged as powerful approaches for probing and characterizing heterogeneous architectures across different scales in complex systems, and a diverse set of methods have yielded fascinating insights into granular materials. In this paper, we review work on network-based approaches to studying granular matter and explore the potential of such frameworks to provide a useful description of these systems and to enhance understanding of their underlying physics. We also outline a few open questions and highlight particularly promising future directions in the analysis and design of granular matter and other kinds of material networks.

The dynamical structure of political corruption networks

Abstract: Corruptive behaviour in politics limits economic growth, embezzles public funds, and promotes socio-economic inequality in modern democracies. We analyse well-documented political corruption scandals in Brazil over the past 27 years, focusing on the dynamical structure of networks where two individuals are connected if they were involved in the same scandal. Our research reveals that corruption runs in small groups that rarely comprise more than eight people, in networks that have hubs and a modular structure that encompasses more than one corruption scandal. We observe abrupt changes in the size of the largest connected component and in the degree distribution, which are due to the coalescence of different modules when new scandals come to light or when governments change. We show further that the dynamical structure of political corruption networks can be used for successfully predicting partners in future scandals. We discuss the important role of network science in detecting and mitigating political corruption.

Network analysis in the legal domain: a complex model for European Union legal sources

Abstract: Legislators, designers of legal information systems, as well as citizens face often problems due to the interdependence of the laws and the growing number of references needed to interpret them. Quantifying this complexity is not an easy task. In this paper, we introduce the "Legislation Network" as a novel approach to address related problems. We have collected an extensive data set of a more than 60-year old legislation corpus, as published in the Official Journal of the European Union, and we further analysed it as a complex network, thus gaining insight into its topological structure. Among other issues, we have performed a temporal analysis of the evolution of the Legislation Network, as well as a robust resilience test to assess its vulnerability under specific cases that may lead to possible breakdowns. Results are quite promising, showing that our approach can lead towards an enhanced explanation in respect to the structure and evolution of legislation properties.

Measuring Partial Balance in Signed Networks

Abstract: Is the enemy of an enemy necessarily a friend, or a friend of a friend a friend? If not, to what extent does this tend to hold? Such questions were formulated in terms of signed (social) networks and necessary and sufficient conditions for a network to be “balanced" were obtained around 1960. Since then the idea that signed networks tend over time to become more balanced has been widely used in several application areas, such as international relations. However investigation of this hypothesis has been complicated by the lack of a standard measure of partial balance, since complete balance is almost never achieved in practice. We formalise the concept of a measure of partial balance, compare several known measures on real-world and synthetic datasets, as well as investigating their axiomatic properties. We use both well-known datasets from the sociology literature, such as Read’s New Guinean tribes, and much more recent ones involving senate bill co-sponsorship. The synthetic data involves both Erdős-Renyi and Barabasi-Albert graphs. We find that under all our measures, real-world networks are more balanced than random networks. We also show that some measures behave better than others in terms of axioms, computational tractability and ability to differentiate between graphs. We make some recommendations for measures to be used in future work.

Centralities of nodes and influences of layers in large multiplex networks

Abstract: We formulate and propose an algorithm (MultiRank) for the ranking of nodes and layers in large multiplex networks. MultiRank takes into account the full multiplex network structure of the data and exploits the dual nature of the network in terms of nodes and layers. The proposed centrality of the layers (influences) and the centrality of the nodes are determined by a coupled set of equations. The basic idea consists in assigning more centrality to nodes that receive links from highly influential layers and from already central nodes. The layers are more influential if highly central nodes are active in them. The algorithm applies to directed/undirected as well as to weighted/unweighted multiplex networks. We discuss the application of MultiRank to three major examples of multiplex network datasets: the European Air Transportation Multiplex Network, the Pierre Auger Multiplex Collaboration Network and the FAO Multiplex Trade Network.

Representation of texts as complex networks: a mesoscopic approach

Abstract: Statistical techniques that analyze texts, referred to as text analytics, have departed from the use of simple word count statistics towards a new paradigm. Text mining now hinges on a more sophisticated set of methods, including the representations in terms of complex networks. While well-established word-adjacency (co-occurrence) methods successfully grasp syntactical features of written texts, they are unable to represent important aspects of textual data, such as its topical structure, i.e. the sequence of subjects developing at a mesoscopic level along the text. Such aspects are often overlooked by current methodologies. In order to grasp the mesoscopic characteristics of semantical content in written texts, we devised a network model which is able to analyze documents in a multi-scale fashion. In the proposed model, a limited amount of adjacent paragraphs are represented as nodes, which are connected whenever they share a minimum semantical content. To illustrate the capabilities of our model, we present, as a case example, a qualitative analysis of "Alice's Adventures in Wonderland". We show that the mesoscopic structure of a document, modeled as a network, reveals many semantic traits of texts. Such an approach paves the way to a myriad of semantic-based applications. In addition, our approach is illustrated in a machine learning context, in which texts are classified among real texts and randomized instances.

Non-backtracking walk centrality for directed networks

Abstract: The theory of zeta functions provides an expression for the generating fu nction of nonbacktracking walk counts on a directed network. We show how this expression can be used to produce a centrality measure that eliminates backtracking walks at no cost. We also show that the radius of convergence of the generating function is determined by the spect rum of a three-by-three block matrix involving the original adjacency matrix. This giv es a means to choose appropriate values of the attenuation parameter. We find that three important a dditional benefits arise when we use this technique to eliminate traversals around the network that are unlikely to be of relevance. First, we obtain a larger range of choices for the attenuation para meter. Second, because the radius of convergence of the generating function is invariant under the remov al of certain types of nodes, we can gain computational efficiencies through reducing the dimension of t he resulting eigenvalue problem. Third, the dimension of the linear system defining the centrali ty measures may be reduced in the same manner. We show that the new centrality measure may be interp reted as standard Katz on a modified network, where self loops are added, and where nonreciproca l edges are augmented with negative weights. We also give a multilayer interpretation, wh ere negatively weighted walks between layers compensate for backtracking walks on the only non-emp ty layer. Studying the limit as the attenuation parameter approaches its upper bound allows us to propose an eigenvector-based nonbacktracking centrality measure in this directed network setting. We find that the two-by-two block matrix arising in previous studies focused on undirected networks must be extended to a new three-by-three block structure to allow for directed edges. We illustrat e the centrality measure on a synthetic network, where it is shown to eliminate a localization effect p resent in standard Katz centrality. Finally, we give results for real networks.

Identifying networks with common organizational principles

Abstract: Many complex systems can be represented as networks, and the problem of network comparison is becoming increasingly relevant. There are many techniques for network comparison, from simply comparing network summary statistics to sophisticated but computationally costly alignment-based approaches. Yet it remains challenging to accurately cluster networks that are of a different size and density, but hypothesized to be structurally similar. In this paper, we address this problem by introducing a new network comparison methodology that is aimed at identifying common organizational principles in networks. The methodology is simple, intuitive and applicable in a wide variety of settings ranging from the functional classification of proteins to tracking the evolution of a world trade network.

Coarse Geometry of Evolving Networks

Abstract: Traditionally, network analysis is based on local properties of vertices, like their degree or clustering, and their statistical behavior across the network in question. This paper develops an approach which is different in two respects: We investigate edge-based properties, and we define global characteristics of networks directly. More concretely, we start with Forman’s notion of the Ricci curvature of a graph, or more generally, a polyhedral complex. This will allow us to pass from a graph as representing a network to a polyhedral complex for instance by filling in triangles into connected triples of edges and to investigate the resulting effect on the curvature. This is insightful for two reasons: First, we can define a curvature flow in order to asymptotically simplify a network and reduce it to its essentials. Second, using a construction of Bloch which yields a discrete Gauß-Bonnet theorem, we have the Euler characteristic of a network as a global characteristic. These two aspects beautifully merge in the sense that the asymptotic properties of the curvature flow are indicated by that Euler characteristic.

Random multi-hopper model : super-fast random walks on graphs

Abstract: We develop a mathematical model considering a random walker with long-range hops on arbitrary graphs. The random multi-hopper can jump to any node of the graph from an initial position, with a probability that decays as a function of the shortest-path distance between the two nodes in the graph. We consider here two decaying functions in the form of Laplace and Mellin transforms of the shortest-path distances. We prove that when the parameters of these transforms approach zero asymptotically, the hitting time in the multi-hopper approaches the minimum possible value for a normal random walker. We show by computational experiments that the multi-hopper explores a graph with clusters or skewed degree distributions more efficiently than a normal random walker. We provide computational evidences of the advantages of the random multi-hopper model with respect to the normal random walk by studying deterministic, random and real-world networks.

A general Markov chain approach for disease and rumour spreading in complex networks

Abstract: Spreading processes are ubiquitous in natural and artificial systems. They can be studied via a plethora of models, depending on the specific details of the phenomena under study. Disease contagion and rumour spreading are among the most important of these processes due to their practical relevance. However, despite the similarities between them, current models address both spreading dynamics separately. In this article, we propose a general spreading model that is based on discrete time Markov chains. The model includes all the transitions that are plausible for both a disease contagion process and rumour propagation. We show that our model not only covers the traditional spreading schemes but that it also contains some features relevant in social dynamics, such as apathy, forgetting, and lost/recovering of interest. The model is evaluated analytically to obtain the spreading thresholds and the early time dynamical behaviour for the contact and reactive processes in several scenarios. Comparison with Monte Carlo simulations shows that the Markov chain formalism is highly accurate while it excels in computational efficiency. We round off our work by showing how the proposed framework can be applied to the study of spreading processes occurring on social networks.

Community structure of copper supply networks in the prehistoric Balkans: An independent evaluation of the archaeological record from the 7th to the 4th millennium BC

Abstract: The dataset includes trace element analyses for 410 copper-based objects from the Balkans (c 7th - 4th mill BC), with PCA scores calculated out of log-normalised values, altogether accompanied with relevant archaeological, chronological and geographical data The article abstract: Complex networks analyses of many physical, biological and social phenomena show remarkable structural regularities, yet, their application in studying human past interaction remains underdeveloped Here, we present an innovative method for identifying community structures in the archaeological record that allow for independent evaluation of the copper using societies in the Balkans, from c 6200 to c 3200 BC We achieve this by exploring modularity of networked systems of these societies across an estimated 3000 years We employ chemical data of copper-based objects from 79 archaeological sites as the independent variable for detecting most densely interconnected sets of nodes with a modularity maximization method Our results reveal three dominant modular structures across the entire period, which exhibit strong spatial and temporal significance We interpret patterns of copper supply among prehistoric societies as reflective of social relations, which emerge as equally important as physical proximity Although designed on a variable isolated from any archaeological and spatiotemporal information, our method provides archaeologically and spatiotemporally meaningful results It produces models of human interaction and cooperation that can be evaluated independently of established archaeological systematics, and can find wide application on any quantitative data from archaeological and historical record

The temporal event graph

Abstract: Temporal networks are increasingly being used to model the interactions of complex systems. Most studies require the temporal aggregation of edges (or events) into discrete time steps to perform analysis. In this article we describe a static, lossless, and unique representation of a temporal network, the temporal event graph (TEG). The TEG describes the temporal network in terms of both the inter-event time and two-event temporal motif distributions. By considering these distributions in unison we provide a new method to characterise the behaviour of individuals and collectives in temporal networks as well as providing a natural decomposition of the network. We illustrate the utility of the TEG by providing examples on both synthetic and real temporal networks.

Modularity of regular and treelike graphs

Abstract: Clustering algorithms for large networks typically use modularity values to test which partitions of the vertex set better represent structure in the data. The modularity of a graph is the maximum ...

Evolutionary prisoner's dilemma games coevolving on adaptive networks.

Abstract: We study a model for switching strategies in the Prisoner's Dilemma game on adaptive networks of player pairings that coevolve as players attempt to maximize their return. We use a node-based strategy model wherein each player follows one strategy at a time (cooperate or defect) across all of its neighbors, changing that strategy and possibly changing partners in response to local changes in the network of player pairing and in the strategies used by connected partners. We compare and contrast numerical simulations with existing pair approximation differential equations for describing this system, as well as more accurate equations developed here using the framework of approximate master equations. We explore the parameter space of the model, demonstrating the relatively high accuracy of the approximate master equations for describing the system observations made from simulations. We study two variations of this partner-switching model to investigate the system evolution, predict stationary states, and compare the total utilities and other qualitative differences between these two model variants.

Optimal curing policy for epidemic spreading over a community network with heterogeneous population

Abstract: The design of an efficient curing policy, able to stem an epidemic process at an affordable cost, has to account for the structure of the population contact network supporting the contagious process. Thus, we tackle the problem of allocating recovery resources among the population, at the lowest cost possible to prevent the epidemic from persisting indefinitely in the network. Specifically, we analyze a susceptible-infected-susceptible epidemic process spreading over a weighted graph, by means of a first-order mean-field approximation. First, we describe the influence of the contact network on the dynamics of the epidemics among a heterogeneous population, that is possibly divided into communities. For the case of a community network, our investigation relies on the graph-theoretical notion of equitable partition; we show that the epidemic threshold, a key measure of the network robustness against epidemic spreading, can be determined using a lower-dimensional dynamical system. Exploiting the computation of the epidemic threshold, we determine a cost-optimal curing policy by solving a convex minimization problem, which possesses a reduced dimension in the case of a community network. Lastly, we consider a two-level optimal curing problem, for which an algorithm is designed with a polynomial time complexity in the network size.

Random walks on the world input–output network

Abstract: Modern production is increasingly fragmented across countries. To disentangle the world production system at sector level, we use the World Input–Output Database to construct the World Input–Output Network (WION) where the nodes are the individual sectors in different countries and the edges are the transactions between them. In order to explore the features and dynamics of the WION, in this article we detect the communities in the WION and evaluate their significance using a random walk Markov chain approach. Our results contribute to the recent stream of literature analysing the role of global value chains in economic integration across countries, by showing global value chains as endogenously emerging communities in the world production system, and discussing how different perspectives produce different results in terms of the pattern of integration.

Weighted random-geometric and random-rectangular graphs: spectral and eigenfunction properties of the adjacency matrix

Abstract: Within a random-matrix-theory approach, we use the nearest-neighbor energy level spacing distribution $P(s)$ and the entropic eigenfunction localization length $\ell$ to study spectral and eigenfunction properties (of adjacency matrices) of weighted random--geometric and random--rectangular graphs. A random--geometric graph (RGG) considers a set of vertices uniformly and independently distributed on the unit square, while for a random--rectangular graph (RRG) the embedding geometry is a rectangle. The RRG model depends on three parameters: The rectangle side lengths $a$ and $1/a$, the connection radius $r$, and the number of vertices $N$. We then study in detail the case $a=1$ which corresponds to weighted RGGs and explore weighted RRGs characterized by $a\sim 1$, i.e.~two-dimensional geometries, but also approach the limit of quasi-one-dimensional wires when $a\gg1$. In general we look for the scaling properties of $P(s)$ and $\ell$ as a function of $a$, $r$ and $N$. We find that the ratio $r/N^\gamma$, with $\gamma(a)\approx -1/2$, fixes the properties of both RGGs and RRGs. Moreover, when $a\ge 10$ we show that spectral and eigenfunction properties of weighted RRGs are universal for the fixed ratio $r/{\cal C}N^\gamma$, with ${\cal C}\approx a$.

Fast link prediction for large networks using spectral embedding

Abstract: Many link prediction algorithms require the computation of a similarity metric on each vertex pair, which is quadratic in the number of vertices and infeasible for large networks. We develop a class of link prediction algorithms based on a spectral embedding and the k closest pairs algorithm that are scalable to very large networks. We compare the prediction accuracy and runtime of these methods to existing algorithms on several large link prediction tasks. Our methods achieve comparable accuracy to standard algorithms but are significantly faster.

A new framework for dynamical models on multiplex networks

Abstract: Many complex systems have natural representations as multi-layer networks. While these formulations retain more information than standard single-layer network models, there is not yet a fully developed theory for computing network metrics and statistics on these objects. We introduce a family of models of multiplex processes motivated by dynamical applications and investigate the properties of their spectra both theoretically and computationally. We study special cases of multiplex diffusion and Markov dynamics, using the spectral results to compute their rates of convergence. We use our framework to define a version of multiplex eigenvector centrality, which generalizes some existing notions in the literature. Last, we compare our operator to structurally-derived models on synthetic and real-world networks, helping delineate the contexts in which the different frameworks are appropriate.

The von Neumann Theil index: characterizing graph centralization using the von Neumann index

Abstract: We show that the von Neumann entropy (from herein referred to as the von Neumann index) of a graph’s trace normalized combinatorial Laplacian provides structural information about the level of centralization across a graph. This is done by considering the Theil index, which is an established statistical measure used to determine levels of inequality across a system of ‘agents’, for example, income levels across a population. Here, we establish a Theil index for graphs, which provides us with a macroscopic measure of graph centralization. Concretely, we show that the von Neumann index can be used to bound the graph’s Theil index, and thus we provide a direct characterization of graph centralization via the von Neumann index. Because of the algebraic similarities between the bound and the Theil index, we call the bound the von Neumann Theil index. We elucidate our ideas by providing examples and a discussion of different n=7 vertex graphs. We also discuss how the von Neumann Theil index provides a more comprehensive measure of centralization when compared to traditional centralization measures, and when compared to the graph’s classical Theil index. This is because it more accurately accounts for macro-structural changes that occur from micro-structural changes in the graph (e.g. the removal of a vertex). Finally, we provide future direction, showing that the von Neumann Theil index can be generalized by considering the Renyi entropy. We then show that this generalization can be used to bound the negative logarithm of the graph’s Jain fairness index.

Two-mode networks exhibiting data loss

Abstract: Motivated by a question arising in the analysis of social networks, we investigate pairs of (0, 1) matrices A,B such that AAT = BBT and AT A = BT B. Using the techniques of combinatorial matrix theory, we show how the problem can be analysed in terms of certain linear systems. We construct two large infinite families of pairs of such matrices. One family has an amusing connection with regular tournament matrices, while the other is connected with a generalisation of Ryser’s notion of an interchange for a (0, 1) matrix. Not surprisingly, both families of matrices are highly structured.

A functional complexity framework for the analysis of telecommunication networks

Abstract: The rapid evolution of network services demands new paradigms for studying and designing networks. In order to understand the underlying mechanisms that provide network functions, we propose a framework which enables the functional analysis of telecommunication networks. This framework allows us to isolate and analyse a network function as a complex system. We propose functional topologies to visualise the relationships between system entities and enable the systematic study of interactions between them. We also define a complexity metric $C_F$ (functional complexity) which quantifies the variety of structural patterns and roles of nodes in the topology. This complexity metric provides a wholly new approach to study the operation of telecommunication networks. We study the relationship between $C_F$ and different graph structures by analysing graph theory metrics in order to recognize complex organisations. $C_F$ is equal to zero for both a full mesh topology and a disconnected topology. We show that complexity is very high for a dense structure that shows high integration (shorter average path length and high average clustering coefficient). We make a connection between functional complexity, robustness and response to changes that may appear in the system configuration. We also make a connection between the implementation and the outcome of a network function which correlates the characteristics of the outcome with the complex relationships that underpin the functional structure.

Network analysis using entropy component analysis

Abstract: Structural complexity measures have found widespread use in network analysis. For instance, entropy can be used to distinguish between different structures. Recently we have reported an approximate network von Neumann entropy measure, which can be conveniently expressed in terms of the degree configurations associated with the vertices that define the edges in both undirected and directed graphs. However, this analysis was posed at the global level, and did not consider in detail how the entropy is distributed across edges. The aim in this paper is to use our previous analysis to define a new characterization of network structure, which captures the distribution of entropy across the edges of a network. Since our entropy is defined in terms of vertex degree values defining an edge, we can histogram the edge entropy using a multi-dimensional array for both undirected and directed networks. Each edge in a network increments the contents of the appropriate bin in the histogram, indexed according to the degree pair in an undirected graph or the in/out-degree quadruple for a directed graph. We normalize the resulting histograms and vectorize them to give network feature vectors reflecting the distribution of entropy across the edges of the network. By performing principal component analysis (PCA) on the feature vectors for samples, we embed populations of graphs into a low-dimensional space. We explore a number of variants of this method, including using both fixed and adaptive binning over edge vertex degree combinations, using both entropy weighted and raw bin-contents, and using multi-linear principal component analysis (MPCA), aimed at extracting the tensorial structure of high-dimensional data, as an alternative to classical PCA for component analysis. We apply the resulting methods to the problem of graph classification, and compare the results obtained to those obtained using some alternative state-of-the-art methods on real-world data.

Mechanisms for tuning clustering and degree-correlations in directed networks

Abstract: With complex networks emerging as an effective tool to tackle multidisciplinary problems, models of network generation have gained an importance of their own. These models allow us to extensively analyze the data obtained from real-world networks, study their relevance and corroborate theoretical results. In this work, we introduce methods, based on degree preserving rewiring, that can be used to tune the clustering and degree-correlations in directed networks with random and scale-free topologies. They provide null-models to investigate the role of the mentioned properties along with their strengths and limitations. We find that in the case of clustering, structural relationships, that are independent of topology and rewiring schemes are revealed, while in the case of degree-correlations, the network topology is found to play an important role in the working of the mechanisms. We also study the effects of link-density on the efficiency of these rewiring mechanisms and find that in the case of clustering, the topology of the network plays an important role in determining how link-density affects the rewiring process, while in the case of degree-correlations, the link-density and topology, play no role for sufficiently large number of rewiring steps. Besides the intended purpose of tuning network properties, the proposed mechanisms can also be used as a tool to reveal structural relationships and topological constraints.

Core-biased random walks in networks

Abstract: A simple strategy to explore a network is to use a random-walk where the walker jumps from one node to an adjacent node at random. It is known that biasing the random jump, the walker can explore every walk of the same length with equal probability, this is known as a Maximal Entropy Random Walk (MERW). To construct a MERW requires the knowledge of the largest eigenvalue λ1 and corresponding eigenvector v (1) of the adjacency matrix A = {aij}, that is global knowledge of the network. When this global information is not available, it is possible to construct a biased random walk which approximates the MERW using only the degree of the nodes, a local property. Here we show that it is also possible to construct a good approximation to a MERW by biasing the random walk via the properties of the network’s core. We present some examples based on real and artificial networks showing that the core-biased random walk outperforms the degree-biased random walks. networks, entropy rate random walks, biased random walk, spectral bound

Labelled network subgraphs reveal stylistic subtleties in written texts

Abstract: The vast amount of data and increase of computational capacity have allowed the analysis of texts from several perspectives, including the representation of texts as complex networks. Nodes of the network represent the words, and edges represent some relationship, usually word co-occurrence. Even though networked representations have been applied to study some tasks, such approaches are not usually combined with traditional models relying upon statistical paradigms. Because networked models are able to grasp textual patterns, we devised a hybrid classifier, called labelled subgraphs, that combines the frequency of common words with small structures found in the topology of the network, known as motifs. Our approach is illustrated in two contexts, authorship attribution and translationese identification. In the former, a set of novels written by different authors is analyzed. To identify translationese, texts from the Canadian Hansard and the European parliament were classified as to original and translated instances. Our results suggest that labelled subgraphs are able to represent texts and it should be further explored in other tasks, such as the analysis of text complexity, language proficiency, and machine translation.