Quantifying randomness in real networks

Orsini, Chiara; Dankulov, Marija Mitrović; Colomer-de-Simón, Pol; Jamakovic, Almerima; Mahadevan, Priya; Vahdat, Amin; Bassler, Kevin E.; Toroczkai, Zoltán; Boguñá, Marián; Caldarelli, Guido; Fortunato, Santo; Krioukov, Dmitri

doi:10.1038/ncomms9627

Cited by 176 publications

(201 citation statements)

References 73 publications

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“…Usually, low-order correlations ( = 2 − 2.5) are sufficient to capture all significant network properties in real world networks. This work has been published recently in the journal Nature Communications [24].…”

Section: The Case For More General Constraints: How Random Are Complementioning

confidence: 98%

Understanding the Fundamental Principles Underlying the Survival and Efficient Recovery of Multi-Scale Techno-Social Networks Following a WMD Event (A)

Toroczkai¹,

Vespignani²

2016

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The public reporting burden for this collection of information is estimated to average 1 hour per respon se. including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information . Send comments regarding this burden estimate or any other aspect of this collection of information. including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information . 1215 Jefferson Davis Highway, Sutte 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstand ing any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currentiy valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM· I. Executive summaryMotivation: Understanding the fundamental principles underlying the functional robustness of Techno-Social Networks (TSN-s) is a tall, but inevitable challenge. As the society becomes increasingly dependent on infrastructure transport networks, the implications of large-scale disruptions (e.g., due to WMD events) of these systems also become increasingly important. In our ever more connected and interdependent world, small perturbations can have far reaching effects. Large-scale events, such as cascading failures (e.g., the East coast blackout on Aug. 14, 2003) or epidemics (SARS and most recently Ebola) are typical to complex networks, and they serve as warnings about the type of behaviors one can expect in strongly interconnected systems. As a result, we demand ever-increasing predictive power and ability to evaluate the impact of potential failures. There has been, however, little to no mathematical and analytical methodology that would allow a realistic assessment of the consequences of large-scale failures in critical infrastructure TSN-s, largely due to two major aspects of these networks: i) Multivariate and heterogeneous constraints. Real-world TSNs typically operate under a wide range of constraints and limitations imposed both from the technical (physical) side and the social (usage) side. Physical constraints include geographical embeddedness; energy limitations (transportation costs, battery life); device capacity, latency and bandwidth, while usage constraints include software limitations, communication protocols and regulations. To advance empirical applications, network models will need to address these constraints since they strongly influence the response and failure modes of a network in case of WMDs. The dynamics of constrained complex networks, especially if they are directed, weighted and hierarchical are not well understood. The adaptive capabilities, including recovery of TSNs facing major destructive events has been a relatively uncharted territory. ii) Multiscale nature. Most of the TSNs are characterized by inherently complex processes involving many different scales in time a...

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Section: The Case For More General Constraints: How Random Are Complementioning

confidence: 98%

Understanding the Fundamental Principles Underlying the Survival and Efficient Recovery of Multi-Scale Techno-Social Networks Following a WMD Event (A)

Toroczkai¹,

Vespignani²

2016

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“…If we impose a network to satisfy some specific properties (i.e., some features), the corresponding RNM complexity is affected by such restrictions [29][30][31]. In [29,30], the concept of network ensembles is proposed, based on a statistical mechanics approach, to characterize random networks.…”

Section: Successive Approximation Modelsmentioning

confidence: 99%

Entropy Characterization of Random Network Models

Zufiria

Barriales-Valbuena

2017

Entropy

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This paper elaborates on the Random Network Model (RNM) as a mathematical framework for modelling and analyzing the generation of complex networks. Such framework allows the analysis of the relationship between several network characterizing features (link density, clustering coefficient, degree distribution, connectivity, etc.) and entropy-based complexity measures, providing new insight on the generation and characterization of random networks. Some theoretical and computational results illustrate the utility of the proposed framework.

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“…The difference in the values for the network-level metrics is attributed to the sociological structure and influence among nodes not being captured in the random networks even though they are modeled to have an identical degree sequence to that of the social networks [48]. The authors in [49] conclude that global network-level metrics cannot be expected to be even closely reproduced in random network graphs generated with local constraints (such as the degree-preserving randomization). To corroborate this statement, degreepreserved randomized versions of the Internet at the level of ASs (AS -Autonomous Systems) are observed to have a fewer number of k-shells [50].…”

Section: Related Workmentioning

confidence: 99%

On the Sufficiency of Using Degree Sequence of the Vertices to Generate Random Networks Corresponding to Real-World Networks

Meghanathan

2016

Polibits

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Abstract-The focus of research in this paper is to investigate whether a random network whose degree sequence of the vertices is the same as the degree sequence of the vertices in a real-world network would exhibit values for other analysis metrics similar to those of the real-world network. We use the well-known Configuration Model to generate a random network on the basis of the degree sequence of the vertices in a real-world network wherein the degree sequence need not be Poisson-style. The extent of similarity between the vertices of the random network and real-world network with respect to a particular metric is evaluated in the form of the correlation coefficient of the values of the vertices for the metric. We involve a total of 24 real-world networks in this study, with the spectral radius ratio for node degree (measure of variation in node degree) ranging from 1.04 to 3.0 (i.e., from random networks to scale-free networks). We consider a suite of seven node-level metrics and three networklevel metrics for our analysis and identify the metrics for which the degree sequence would be just sufficient to generate random networks that have a very strong correlation (correlation coefficient of 0.8 or above) with that of the vertices in the corresponding real-world networks.Index Terms-Configuration model, degree sequence, correlation, random network, real-world network. I. INTRODUCTIONANDOM networks are a class of complex networks in which there could be link between any two nodes in the network. The Erdos-Renyi (ER) model [1] is a commonly used theoretical model for generating random networks. The ER model-based random networks are characteristic of exhibiting a Poisson-style [2] degree sequence such that the degree of any vertex is typically very close to the average degree of the vertices in the network (i.e., the variation in node degree is typically low). However, the degree sequence of most of the real-world networks rarely follows a Poissonstyle distribution; there usually exists an appreciable amount of variation in node degree [3] and there could also be preferential attachment with selected nodes rather than arbitrary attachment [4]. Figure 1 shows the degree sequence of the well-known real-world networks with N nodes and L edges and the corresponding ER model-based random networks generated with a probability of link value of 2L/{N(N-1)} [5]. Due to the inherent differences in the nature of the degree sequence, the values for several node-level metrics and network-level metrics exhibited by a ER modelbased random network with a certain number of nodes and edges are likely to be independent (correlation coefficient is close to 0) to that of the metric values exhibited by a realworld network with the same number of nodes and edges [5]. In this research, we explore whether a random network whose degree sequence matches to that of a real-world network could exhibit similar values for several critical nodelevel and network-level metrics as that of the real-world network. In this pursuit, we chose to use...

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Quantifying randomness in real networks

Cited by 176 publications

References 73 publications

Understanding the Fundamental Principles Underlying the Survival and Efficient Recovery of Multi-Scale Techno-Social Networks Following a WMD Event (A)

Understanding the Fundamental Principles Underlying the Survival and Efficient Recovery of Multi-Scale Techno-Social Networks Following a WMD Event (A)

Entropy Characterization of Random Network Models

On the Sufficiency of Using Degree Sequence of the Vertices to Generate Random Networks Corresponding to Real-World Networks

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