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Journal ArticleDOI

Network sampling and classification: An investigation of network model representations

01 Jun 2011-Vol. 51, Iss: 3, pp 506-518

TL;DR: It is argued that conclusions based on simulated network studies must focus on the full features of the connectivity patterns of a network instead of on the limited set of network metrics for a specific network type.

AbstractMethods for generating a random sample of networks with desired properties are important tools for the analysis of social, biological, and information networks. Algorithm-based approaches to sampling networks have received a great deal of attention in recent literature. Most of these algorithms are based on simple intuitions that associate the full features of connectivity patterns with specific values of only one or two network metrics. Substantive conclusions are crucially dependent on this association holding true. However, the extent to which this simple intuition holds true is not yet known. In this paper, we examine the association between the connectivity patterns that a network sampling algorithm aims to generate and the connectivity patterns of the generated networks, measured by an existing set of popular network metrics. We find that different network sampling algorithms can yield networks with similar connectivity patterns. We also find that the alternative algorithms for the same connectivity pattern can yield networks with different connectivity patterns. We argue that conclusions based on simulated network studies must focus on the full features of the connectivity patterns of a network instead of on the limited set of networkmetrics for a specific network type. This fact has important implications for network data analysis: for instance, implications related to the way significance is currently assessed.

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Citations
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Journal ArticleDOI
Abstract: We leverage the newly emerging business analytical capability to rapidly deploy and iterate large-scale, microlevel, in vivo randomized experiments to understand how social influence in networks impacts consumer demand. Understanding peer influence is critical to estimating product demand and diffusion, creating effective viral marketing, and designing “network interventions” to promote positive social change. But several statistical challenges make it difficult to econometrically identify peer influence in networks. Though some recent studies use experiments to identify influence, they have not investigated the social or structural conditions under which influence is strongest. By randomly manipulating messages sent by adopters of a Facebook application to their 1.3 million peers, we identify the moderating effect of tie strength and structural embeddedness on the strength of peer influence. We find that both embeddedness and tie strength increase influence. However, the amount of physical interaction between friends, measured by coappearance in photos, does not have an effect. This work presents some of the first large-scale in vivo experimental evidence investigating the social and structural moderators of peer influence in networks. The methods and results could enable more effective marketing strategies and social policy built around a new understanding of how social structure and peer influence spread behaviors in society. This paper was accepted by Alok Gupta, special issue on business analytics.

259 citations


Journal ArticleDOI
TL;DR: This study examines the impact of global supply network structure on risk diffusion and supply network health and demonstrates the importance of supply network visibility, and indicates that small-world supply network topologies consistently outperform supply networks with scale-free characteristics.
Abstract: Understanding and managing supply chain risks is a critical functional competency for today's global enterprises. A lack of this competency can have significant negative outcomes, including costly production and delivery delays, loss of future sales, and a tarnished corporate image. The ability to identify and mitigate risks, however, is complicated as supply chains are becoming increasingly global, complex, and interconnected. Drawing on the complex systems and epidemiology literature, and using a computational modeling and network analysis approach, we examine the impact of global supply network structure on risk diffusion and supply network health and demonstrate the importance of supply network visibility. Our results show a significant association between network structure and both risk diffusion and supply network health. In particular, our results indicate that small-world supply network topologies consistently outperform supply networks with scale-free characteristics. Theoretically, our study contributes to our understanding of risk management and supply networks as complex networked systems using a computational approach. Managerially, our study illustrates how decision makers can benefit from a network analytic approach to develop a more holistic understanding of system-wide risk diffusion and to guide network governance policies for more favorable health level outcomes. The article concludes by highlighting the main findings and discussing possibilities of future research directions.

101 citations


Proceedings Article
21 Jun 2014
TL;DR: A histogram estimator of a graphon that is provably consistent and numerically efficient is proposed, based on a sorting-and-smoothing (SAS) algorithm, which first sorts the empirical degree of agraph, then smooths the sorted graph using total variation minimization.
Abstract: Exchangeable graph models (ExGM) subsume a number of popular network models. The mathematical object that characterizes an ExGM is termed a graphon. Finding scalable estimators of graphons, provably consistent, remains an open issue. In this paper, we propose a histogram estimator of a graphon that is provably consistent and numerically efficient. The proposed estimator is based on a sorting-and-smoothing (SAS) algorithm, which first sorts the empirical degree of a graph, then smooths the sorted graph using total variation minimization. The consistency of the SAS algorithm is proved by leveraging sparsity concepts from compressed sensing.

71 citations


Cites methods from "Network sampling and classification..."

  • ...Developing statistical models for network data has been a growing research area in statistics and machine learning over the past decade (Goldenberg et al., 2009; Kolaczyk, 2009; Airoldi et al., 2011)....

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Journal ArticleDOI
01 Nov 2014
TL;DR: The study provides macroscopic view of supply network risk issues across multiple tiers, grounded in theories of supply chains as complex systems, network analysis, and risk management, and demonstrates the importance of visual decision support for supply networkrisk assessment.
Abstract: In today's complex, global supply networks it has become increasingly challenging to identify, evaluate, and mitigate risks of disruption. Traditional supply chain practices have primarily focused on dyadic risk management, rarely considering risks in the sub-tier supply network. However, this approach severely limits a decision maker's ability to understand the highly interconnected nature of systemic risks and develop corresponding mitigation strategies. Grounded in theories of supply chains as complex systems, network analysis, and risk management, we demonstrate the importance of visual decision support for supply network risk assessment. We empirically illustrate our approach with supply network visualization examples from the electronics industry. We conclude the study with implications for the design and implementation of visual supply network decision support systems and future research opportunities. A visual network analytic approach allows mapping of flow, information, and risk.Subtier risk is prevalent in electronics industry and distributions differ by tier.The study provides macroscopic view of supply network risk issues across multiple tiers.Multiple visual depictions reveal distribution of risk levels across supply network.Integrating depictions enables timely identification of dependencies and risks.

47 citations


Journal ArticleDOI
TL;DR: This research effort investigates the relationship between network characteristics and supply chain resilience and demonstrates that utilizing a reduced list of characteristics yields performance equal to that when using a complete set of characteristics.
Abstract: Inspired by the fact that a combination of network characteristics can describe a network more fully than the network type is able to, especially since some networks do not belong to any one specific type, this research effort investigates the relationship between network characteristics and supply chain resilience. We begin by demonstrating that the investigation of network characteristics can lead to a better understanding of supply chain resilience. We then identify the key network characteristics that best represent network structure in determining resilience. We show that utilizing a reduced list of characteristics yields performance equal to that when using a complete set of characteristics. Based on the results, we summarize key points that can support interpretation of the impact of network characteristics on resilience. We also conduct a case study to illustrate how our approach can be employed to understand resilience.

43 citations


References
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Journal ArticleDOI
04 Jun 1998-Nature
TL;DR: Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.
Abstract: Networks of coupled dynamical systems have been used to model biological oscillators, Josephson junction arrays, excitable media, neural networks, spatial games, genetic control networks and many other self-organizing systems. Ordinarily, the connection topology is assumed to be either completely regular or completely random. But many biological, technological and social networks lie somewhere between these two extremes. Here we explore simple models of networks that can be tuned through this middle ground: regular networks 'rewired' to introduce increasing amounts of disorder. We find that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. We call them 'small-world' networks, by analogy with the small-world phenomenon (popularly known as six degrees of separation. The neural network of the worm Caenorhabditis elegans, the power grid of the western United States, and the collaboration graph of film actors are shown to be small-world networks. Models of dynamical systems with small-world coupling display enhanced signal-propagation speed, computational power, and synchronizability. In particular, infectious diseases spread more easily in small-world networks than in regular lattices.

35,972 citations


"Network sampling and classification..." refers background in this paper

  • ...An analysis would then claim, for example, that scale-free networks are characterized by having a power-law degree distribution [40]....

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  • ...[33], and it “sounds” like a plausible explanation [33,40]....

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  • ...Small world [40] Θ=(n,k,pn) Nodes, neighbors, pr rewire 2....

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  • ...Algorithm-based approaches to sampling networks [3,34,40] have received a great deal of attention in recent literature [9,11,15,30,41]....

    [...]

  • ...(Small world) Each node is connected to several of its neighbors and a few distant nodes, according to the ring-induced distance [40] (Fig....

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Journal ArticleDOI
15 Oct 1999-Science
TL;DR: A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
Abstract: Systems as diverse as genetic networks or the World Wide Web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This feature was found to be a consequence of two generic mechanisms: (i) networks expand continuously by the addition of new vertices, and (ii) new vertices attach preferentially to sites that are already well connected. A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.

30,921 citations


"Network sampling and classification..." refers background in this paper

  • ...Scale free [7] Θ=(n,n0,p0,pn) Nodes, init nodes, pr init edge, pr edge 4....

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Book
28 Jul 2013
Abstract: During the past decade there has been an explosion in computation and information technology. With it have come vast amounts of data in a variety of fields such as medicine, biology, finance, and marketing. The challenge of understanding these data has led to the development of new tools in the field of statistics, and spawned new areas such as data mining, machine learning, and bioinformatics. Many of these tools have common underpinnings but are often expressed with different terminology. This book describes the important ideas in these areas in a common conceptual framework. While the approach is statistical, the emphasis is on concepts rather than mathematics. Many examples are given, with a liberal use of color graphics. It is a valuable resource for statisticians and anyone interested in data mining in science or industry. The book's coverage is broad, from supervised learning (prediction) to unsupervised learning. The many topics include neural networks, support vector machines, classification trees and boosting---the first comprehensive treatment of this topic in any book. This major new edition features many topics not covered in the original, including graphical models, random forests, ensemble methods, least angle regression and path algorithms for the lasso, non-negative matrix factorization, and spectral clustering. There is also a chapter on methods for ``wide'' data (p bigger than n), including multiple testing and false discovery rates. Trevor Hastie, Robert Tibshirani, and Jerome Friedman are professors of statistics at Stanford University. They are prominent researchers in this area: Hastie and Tibshirani developed generalized additive models and wrote a popular book of that title. Hastie co-developed much of the statistical modeling software and environment in R/S-PLUS and invented principal curves and surfaces. Tibshirani proposed the lasso and is co-author of the very successful An Introduction to the Bootstrap. Friedman is the co-inventor of many data-mining tools including CART, MARS, projection pursuit and gradient boosting.

18,981 citations


Journal ArticleDOI
Abstract: The emergence of order in natural systems is a constant source of inspiration for both physical and biological sciences. While the spatial order characterizing for example the crystals has been the basis of many advances in contemporary physics, most complex systems in nature do not offer such high degree of order. Many of these systems form complex networks whose nodes are the elements of the system and edges represent the interactions between them. Traditionally complex networks have been described by the random graph theory founded in 1959 by Paul Erdohs and Alfred Renyi. One of the defining features of random graphs is that they are statistically homogeneous, and their degree distribution (characterizing the spread in the number of edges starting from a node) is a Poisson distribution. In contrast, recent empirical studies, including the work of our group, indicate that the topology of real networks is much richer than that of random graphs. In particular, the degree distribution of real networks is a power-law, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network. The scale-free topology of real networks has very important consequences on their functioning. For example, we have discovered that scale-free networks are extremely resilient to the random disruption of their nodes. On the other hand, the selective removal of the nodes with highest degree induces a rapid breakdown of the network to isolated subparts that cannot communicate with each other. The non-trivial scaling of the degree distribution of real networks is also an indication of their assembly and evolution. Indeed, our modeling studies have shown us that there are general principles governing the evolution of networks. Most networks start from a small seed and grow by the addition of new nodes which attach to the nodes already in the system. This process obeys preferential attachment: the new nodes are more likely to connect to nodes with already high degree. We have proposed a simple model based on these two principles wich was able to reproduce the power-law degree distribution of real networks. Perhaps even more importantly, this model paved the way to a new paradigm of network modeling, trying to capture the evolution of networks, not just their static topology.

17,463 citations


Book
25 Nov 1994
TL;DR: This paper presents mathematical representation of social networks in the social and behavioral sciences through the lens of Dyadic and Triadic Interaction Models, which describes the relationships between actor and group measures and the structure of networks.
Abstract: Part I. Introduction: Networks, Relations, and Structure: 1. Relations and networks in the social and behavioral sciences 2. Social network data: collection and application Part II. Mathematical Representations of Social Networks: 3. Notation 4. Graphs and matrixes Part III. Structural and Locational Properties: 5. Centrality, prestige, and related actor and group measures 6. Structural balance, clusterability, and transitivity 7. Cohesive subgroups 8. Affiliations, co-memberships, and overlapping subgroups Part IV. Roles and Positions: 9. Structural equivalence 10. Blockmodels 11. Relational algebras 12. Network positions and roles Part V. Dyadic and Triadic Methods: 13. Dyads 14. Triads Part VI. Statistical Dyadic Interaction Models: 15. Statistical analysis of single relational networks 16. Stochastic blockmodels and goodness-of-fit indices Part VII. Epilogue: 17. Future directions.

17,092 citations