Showing papers in "Journal of Complex Networks in 2014"

Analysis of critical and redundant nodes in controlling directed and undirected complex networks using dominating sets

Abstract: Recent studies have drawn attention to the problem of how complex networks can be controlled through a small number of controller nodes. Here, we develop an algorithmic procedure and mathematical tools to compute and evaluate the critical and redundant nodes in controlling directed and undirected scalefree networks using the minimum dominating set (MDS) approach. Because there are multiple MDS configurations that control the entire network, we can classify the nodes depending on the condition whether a node is part of all (critical), some but not all (intermittent), or does not participate in any (redundant) possible MDS. The presented mathematical analysis predicts the probability of finding a critical node in undirected scale-free networks with k−γ , where k is a node degree, as a function of the scaling exponent γ and its node degree. Critical nodes tend to have high degree and are more abundant in undirected scale-free networks with high γ . In addition, analytical expressions of lower bounds for the number of critical nodes for both undirected and directed networks are also derived. By applying the MDS control model, we find that undirected networks can be controlled with relatively fewer nodes than those engaged in controlling directed networks. On the other hand, our computational experiments also show that the MDS is unimodal with varying the average degree 〈k〉 in both directed and undirected networks. In particular, by increasing 〈k〉, the fraction of nodes engaged in control becomes smaller, which highlights a centralized control mode. The analysis of a set of undirected and directed real-world networks confirms the findings shown in theoretical analysis and simulation experiments.

Percolation and cascade dynamics of spatial networks with partial dependency

Abstract: Recently, it has been shown that the removal of a random fraction of nodes from a system of interdependent spatial networks can lead to cascading failures which amplify the original damage and destroy the entire system, often via abrupt first-order transitions. For these distinctive phenomena to emerge, the interdependence between networks need not be total. We consider here a system of partially interdependent spatial networks (modelled as lattices) with a fraction q of the nodes interdependent and the remaining 1 − q autonomous. In our model, the dependency links between networks are of geometric length less than r. Under full dependency (q = 1), this system was shown to have a first-order percolation transition if r > rc ≈ 8. Here, we generalize this result and show that for all q > 0, there will be a first-order transition if r > rc(q). We show that rc(q) increases monotonically with decreasing q and limq→0+ rc(q) = ∞. Additionally, we present a detailed description and explanation of the cascading failures in spatially embedded interdependent networks near the percolation threshold pc. These failures follow three mechanisms depending on the value of r. Below rc the system undergoes a continuous transition similar to standard percolation on a lattice. Above rc there are two distinct first-order transitions for finite and infinite r, respectively. The cascading failure for finite r is characterized by the emergence of a critical hole which then spreads through the system while the infinite r transition is more similar to the case of random networks. Surprisingly, we find that this spreading transition can still occur even if p < pc. We present measurements of cascade dynamics which differentiate between these phase transitions and elucidate their mechanisms. These results extend previous research on spatial networks to the more realistic case of partial dependency and shed new light on the specific dynamics of dependencydriven cascading failures.

Community detection: effective evaluation on large social networks

Abstract: While many recently proposed methods aim to detect network communities in large datasets, such as those generated by social media and telecommunications services, most evaluation (i.e. benchmarking) of this research is based on small, hand-curated datasets. We argue that these two types of networks differ so significantly that, by evaluating algorithms solely on the smaller networks, we know little about how well they perform on the larger datasets. Recent work addresses this problem by introducing social network datasets annotated with meta-data that is believed to approximately indicate a ‘ground truth’ set of network communities. While such efforts are a step in the right direction, we find this meta-data problematic for two reasons. First, in practice, the groups contained in such meta-data may only be a subset of a network’s communities. Second, while it is often reasonable to assume that meta-data is related to network communities in some way, we must be cautious about assuming that these groups correspond closely to network communities. Here, we consider these difficulties and propose an evaluation scheme based on a classification task that is tailored to deal with them.

Oriented and degree-generated block models: generating and inferring communities with inhomogeneous degree distributions

Abstract: The stochastic block model is a powerful tool for inferring community structure from network topology. However, it predicts a Poisson degree distribution within each community, while most real-world networks have a heavy-tailed degree distribution. The degree-corrected block model can accommodate arbitrary degree distributions within communities. 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. In this paper, we present 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.

First-principles multiway spectral partitioning of graphs

Abstract: We consider the minimum-cut partitioning of a graph into more than two parts using spectral methods. While there exist well-established spectral algorithms for this problem that give good results, they have traditionally not been well motivated. Rather than being derived from first principles by minimizing graph cuts, they are typically presented without direct derivation and then proved after the fact to work. In this paper, we take a contrasting approach in which we start with a matrix formulation of the minimum cut problem and then show, via a relaxed optimization, how it can be mapped onto a spectral embedding defined by the leading eigenvectors of the graph Laplacian. The end result is an algorithm that is similar in spirit to, but different in detail from, previous spectral partitioning approaches. In tests of the algorithm we find that it outperforms previous approaches on certain particularly difficult partitioning problems.

Critical transitions in social network activity

Abstract: A large variety of complex systems in ecology, climate science, biomedicine and engineering have been observed to exhibit tipping points, where the internal dynamical state of the system abruptly changes. For example, such critical transitions may result in the sudden change of ecological environments and climate conditions. Data and models suggest that some of these drastic events may be preceded by detectable early-warning signs. This view is also corroborated by abstract mathematical theory for generic bifurcations in stochastic multi-scale systems. Whether early-warnings are also present in social networks that anticipate a-priori unknown events in society is an open problem to which only highly speculative answers can be given at present. Here, we focus on a-priori known events and analyze a social network data set with a focus on classical variance and autocorrelation warning signs. We find that several a-priori known events are preceded by variance and autocorrelation growth as predicted by mathematical theory.

Stochastic trade networks

Abstract: This paper develops a simple network model to describe the dynamic of the intensive and extensive margin of international trade flows. The result is achieved by means of the combination of two mechanisms of proportional growth: the first (discrete) determines the formation of trade links, the second (continuous) governs trade intensity. We show that our setup is able to simultaneously match a large number of empirical regularities, such as the fraction of zero trade flows across pairs of countries or the high concentration of trade with respect to both products and destinations. Our findings suggest that stylized facts are strongly interconnected across different levels of aggregation of trade data , so that a unifying explanation is called for. By incorporating stochastic elements into standard trade models we can improve their ability to explain relevant facts about world trade.

On global stability of financial networks

Abstract: The recent financial crisis have generated renewed interests in fragilities of global financial networks among economists and regulatory authorities. In particular, a potential vulnerability of the financial networks is the "financial contagion" process in which insolvencies of individual entities propagate through the "web of dependencies" to affect the entire system. In this paper, we formalize an extension of a financial network model originally proposed by Nier et al. for scenarios such as the OTC derivatives market, define a suitable global stability measure for this model, and perform a comprehensive empirical evaluation of this stability measure over more than 700,000 combinations of networks types and parameter combinations. Based on our evaluations, we discover many interesting implications of our evaluations of this stability measure, and derive topological properties and parameters combinations that may be used to flag the network as a possible fragile network. An interactive software FIN-STAB for computing the stability is available from the website www2.cs.uic.edu/~dasgupta/financial-simulator-files

Robustness of skeletons and salient features in networks

Abstract: Summary of the networks. Presented here : N , the number of nodes in the network ; L , the number of links ; k , the average degree ;CV (k) the coefficient of variation of degree ;CV (w) , the coefficient of variation of weight ; ρ = L/ N 2 , the network density and r , the degreeassortativity coefficient. The coefficients of variation CV (w) and CV (k) are defined as the ratioof the standard deviation , σ , to the mean , μ , of the weight and degree populations , respectively Network NL k ρ CV (k) CV (w) r Airport 1227 18050 29.42 0.024 1.29 2.25 −0.06Migration 3056 71551 46.83 0.015 1.94 6.13 −0.06Cargo 951 25819 54.30 0.057 1.22 6.85 −0.14Neural 297 2141 14.46 0.049 0.89 1.35 −0.16Food Web 121 1763 29.14 0.24 0.45 11.77 −0.10Metabolic 311 1304 8.39 0.027 1.79 7.91 −0.25Random 1000 15028 30.06 0.03 0.177 1.44 −0.005greater availability of large datasets [6]. The brain’s neurons have been mapped using these methods[7], as have air traffic patterns [8], and the flow of cargo throughout the world [9].The explosion of research on complex networks in recent years has led to the discovery of variousproperties of networks and has allowed us to find ways of reducing the complexity while preservingcertain key features. Many of these methods focus on reducing the number of nodes in the network.Aside from simple thresholding, more sophisticated coarse-graining techniques have also been used[10] to reduce the number of distinct entities in the network. Here, we will focus on methods of reducingthe number of links in the network while preserving the nodes. This is advantageous since it reduces thecomplexity of the system while still preserving scale-free properties.Further, there has been considerable effort in understanding how networks as a whole respond todamage [11–14]. These studies have explored different methods of perturbing the network such asintentional attack and random failure.Despite the significant amount of research in both of these areas separately, there has been littlework in combining the study of backbone and skeleton methods with stress applied to the system. Here,we examine how skeletons and backbones respond to different methods of stress applied to the system.1.1

A uniform random graph model for directed acyclic networks and its effect on motif-finding

Abstract: Random graph models are commonly used as a null-hypothesis in the study of real-world networks. It is important that these networks resemble the real network under study, since they are used to deduce the significance of specific properties of the real network. Existing random graph models introduce unwanted features such as multiple edges and directed cycles when randomizing directed acyclic networks. This paper proposes a new random graph model for directed acyclic networks which overcomes these shortcomings. This ordered switching method is shown to sample uniformly from a suitable graph ensemble. After introducing this method, its use in motif-finding experiments is investigated. Even though the new and existing random network models result in networks with different properties, the patterns that are identified as network motifs in the two citation networks examined in this paper do not depend on the choice of null-model. However, when using the commonly used switching model as a null-model, sometimes anti-motifs are found that contain directed cycles, which is not the case when the ordered switching method is used. The ordered switching method is the first random graph model for directed acyclic networks that takes into account the degree sequences, topological ordering and does not introduce multiple edges, and should therefore have many applications in the study of directed acyclic networks.

Detecting events in the dynamics of ego-centred measurements of the Internet topology

Abstract: Detecting events such as major routing changes or congestions in the dynamics of the internet topology is an important but challenging task. We explore here an empirical approach based on a notion of statistically significant events. It consists in identifying properties of graph dynamics which exhibit a homogeneous distribution with outliers, corresponding to events. We apply this approach to ego-centered measurements of the internet topology (views obtained from a single monitor) and show that it succeeds in detecting meaningful events. Finally, we give some hints for the interpretation of detected events in terms of network operations.

Network null-model based on maximal entropy and the rich-club

Abstract: We present a method to construct a network null-model based on the maximum entropy principle and where the restrictions that the rich-club and the degree sequence impose are conserved. We show that the probability that two nodes share a link can be described with a simple probability function. The null-model closely approximates the assortative properties of the network.

Generating online social networks based on socio-demographic attributes

Abstract: Recent years have seen tremendous growth of many online social networks such as Facebook, LinkedIn and MySpace. People connect to each other through these networks forming large social communities providing researchers rich datasets to understand, model and predict social interactions and behaviors. New contacts in these networks can be formed due to an individual's demographic attributes such as age group, gender, geographic location, or due to a network's structural dynamics such as triadic closure and preferential attachment, or a combination of both demographic and structural characteristics. A number of network generation models have been proposed in the last decade to explain the structure, evolution and processes taking place in different types of networks, and notably social networks. Network generation models studied in the literature primarily consider structural properties, and in some cases an individual's demographic profile in the formation of new social contacts. These models do not present a mechanism to combine both structural and demographic characteristics for the formation of new links. In this paper, we propose a new network generation algorithm which incorporates both these characteristics to model network formation. We use different publicly available Facebook datasets as benchmarks to demonstrate the correctness of the proposed network generation model. The proposed model is flexible and thus can generate networks with varying demographic and structural properties.

Weighted betweenness and algebraic connectivity

Abstract: One of the better studied topology metrics of complex networks is the second smallest eigenvalue of the Laplacian matrix of a network’s graph, referred to as the algebraic connectivity mN-1. This spectral metric plays a decisive role in synchronization of coupled oscillators, network robustness, consensus problems, belief propagation, graph partitioning, and distributed filtering in sensor networks. However, computing the graph spectra is computationally slow and its convergence greatly depends on the topology, thus a number of lower bounds have been proposed over the years in order to find good approximations. To date, the closest bound is the one proposed by Rad et al. [21] in 2009. The current paper proposes new approximations for the algebraic connectivity based on three variations of the betweenness centrality, a popular centrality score often used in social studies to characterize the importance of a node or link within a network. Based on numerical and a partly analytic analysis, we show that our approximations provide accurate lower bounds for the algebraic connectivity for a wide range of graphs, including random, power-law, small-world, and lattice graphs. In particular, we numerically show that the average weighted Brandes betweenness can be treated as a lower bound for large enough networks, which greatly improves state-of-the-art bounds.

Border sensitive centrality in global patent citation networks

Abstract: When resources are shared between interacting networks, the importance of each node depends strongly on how collaborative or competitive each sub-network is. In this paper, we develop a new method of measuring centrality in the complex network of patent citations that can take political borders into account, where the national benefit of domestic citations relative to foreign citations can be controlled by a free parameter. We find that while some patent classes are of high importance both in the global and the domestic economy, there often exist patent classes in individual countries that are more central nationally than in global economy. We characterize the most important classes globally and domestically for six different nations, and describe their robustness to various perturbations to the model and to noise.

Using the network reliability polynomial to characterize and design networks

Abstract: We consider methods for solving certain network characterization and design problems that arise in network epidemiology. We argue that the network reliability polynomial introduced by Moore and Shannon is a useful framework in which to reason about these problems. Specifically, we show how efficient estimation of the polynomial permits characterizing and distinguishing very large networks in ways that are are dynamically relevant. Furthermore, a generalization of flows and cuts to structures that determine the reliability suggests a new measure of edge or vertex centrality that we call criticality. We describe how criticality is related to the more common notion of betweenness and illustrate its application to targeting interventions to control outbreaks of infectious disease. Although our applications are to infectious disease outbreaks, the methods we develop are applicable to many other diffusive dynamical systems over complex networks.

Primary evolving networks and the comparative analysis of robust and fragile structures

Abstract: In this paper we consider the structure of dynamically evolving networks modelling information and activity moving across a large set of vertices. We adopt the communicability concept that generalizes that of centrality which is defined for static networks. We define the primary network structure within the whole as comprising of the most influential vertices (both as senders and receivers of dynamically sequenced activity). We present a methodology based on successive vertex knockouts, up to a very small fraction of the whole primary network,that can characterize the nature of the primary network as being either relatively robust and lattice-like (with redundancies built in) or relatively fragile and tree-like (with sensitivities and few redundancies). We apply these ideas to the analysis of evolving networks derived from fMRI scans of resting human brains. We show that the estimation of performance parameters via the structure tests of the corresponding primary networks is subject to less variability than that observed across a very large population of such scans. Hence the differences within the population are significant.

Network parameters and heuristics in practice: a case study using the target set selection problem

Abstract: It is well known that many real-world networks (‘complex’ networks), such as social, biological and communication networks, have distinctive topological features. However, in general, it is an open question whether or not these features can provide any algorithmic benefits. In this paper, we introduce ideas from the area of parametrized complexity to try and provide a partial answer to this question. We investigate the values of some of the parameters commonly employed by the parametrized complexity community in a range of real social, biological and communication networks. In all cases, the parameter values are much too high to be of practical use. Because of this lack of tractability in practice, we investigate dynamic strategies for exploiting the distinctive topological features of real-world networks to improve the prospects for efficient computation of acceptable problem solutions, using both fixed-parameter and greedy approaches. Our strategies involve simple targeted operations: vertex deletion and edge addition, which could easily be applied in cases such as social networks. As a case study, we consider the target set selection problem, a ubiquitous problem that models many problems concerning the spread of information in networks.