What network motifs tell us about resilience and reliability of complex networks

Significance Networks provide useful models for many natural and manmade phenomena, such as transportation, financial, and social–ecological systems. This paper addresses network motifs as a mechanism for understanding resilience of such networks. The significance of this work can be viewed through an important example—namely, power-grid networks, constituting a core component of modern critical infrastructures. While most existing approaches focus on the analysis of global network characteristics, recent studies suggest that resilience of power grids may also be intrinsically connected to higher-order geometric features such as network motifs. Here, a systematic data-driven approach is developed that sheds light on the role of local topology and geometry in vulnerability of power grids and other complex networks. Network motifs are often called the building blocks of networks. Analysis of motifs has been found to be an indispensable tool for understanding local network structure, in contrast to measures based on node degree distribution and its functions that primarily address a global network topology. As a result, networks that are similar in terms of global topological properties may differ noticeably at a local level. This phenomenon of the impact of local structure has been recently documented in network fragility analysis and classification. At the same time, many studies of networks still tend to focus on global topological measures, often failing to unveil hidden mechanisms behind vulnerability of real networks and their dynamic response to malfunctions. In this paper, a study of motif-based analysis of network resilience and reliability under various types of intentional attacks is presented, with the goal of shedding light on local dynamics and vulnerability of networks. These methods are demonstrated on electricity transmission networks of 4 European countries, and the results are compared with commonly used resilience and reliability measures.

[1]  J. Ser,et al.  A Critical Review of Robustness in Power Grids Using Complex Networks Concepts , 2015 .

[2]  Martí Rosas-Casals,et al.  Assessing European power grid reliability by means of topological measures , 2009 .

[3]  Bo Henry Lindqvist,et al.  Mathematical and statistical methods in reliability , 2003 .

[4]  Jobst Heitzig,et al.  How dead ends undermine power grid stability , 2014, Nature Communications.

[5]  Francisco J. Samaniego,et al.  Linking Dominations and Signatures in Network Reliability , 2002 .

[6]  Ryan A. Rossi,et al.  Graphlet decomposition: framework, algorithms, and applications , 2015, Knowledge and Information Systems.

[7]  J. Coresh,et al.  Adjusting survival curves for confounders: a review and a new method. , 1996, American journal of epidemiology.

[8]  Amin Abedi,et al.  Review of major approaches to analyze vulnerability in power system , 2019, Reliab. Eng. Syst. Saf..

[9]  Nozer D. Singpurwalla,et al.  Reliability and risk , 2006 .

[10]  Marco Aiello,et al.  The Power Grid as a Complex Network: a Survey , 2011, ArXiv.

[11]  Olgica Milenkovic,et al.  Inhomogeneous Hypergraph Clustering with Applications , 2017, NIPS.

[12]  Guido Caldarelli,et al.  Islanding the power grid on the transmission level: less connections for more security , 2016, Scientific Reports.

[13]  David W. Hosmer,et al.  Applied Survival Analysis: Regression Modeling of Time-to-Event Data , 2008 .

[14]  Jerald F. Lawless,et al.  Statistical Models and Methods for Lifetime Data: Lawless/Statistical , 2002 .

[15]  Han Fei,et al.  Vertical Vibrations of Suspension Bridges: A Review and a New Method , 2020, Archives of Computational Methods in Engineering.

[16]  P. V. Rao,et al.  Applied Survival Analysis: Regression Modeling of Time to Event Data , 2000 .

[17]  Murat Kantarcioglu,et al.  Forecasting Bitcoin Price with Graph Chainlets , 2018, PAKDD.

[18]  H. Vincent Poor,et al.  Motif-based analysis of power grid robustness under attacks , 2017, 2017 IEEE Global Conference on Signal and Information Processing (GlobalSIP).

[19]  Natasa Przulj,et al.  Biological network comparison using graphlet degree distribution , 2007, Bioinform..

[20]  A. F. Adams,et al.  The Survey , 2021, Dyslexia in Higher Education.

[21]  Francisco J. Samaniego,et al.  LINKING DOMINATIONS AND SIGNATURES IN NETWORK RELIABILITY THEORY , 2003 .

[22]  F. Samaniego,et al.  The signature of a coherent system and its application to comparisons among systems , 1999 .

[23]  Massimo Marchiori,et al.  Error and attacktolerance of complex network s , 2004 .

[24]  Regina Y. Liu,et al.  Multivariate analysis by data depth: descriptive statistics, graphics and inference, (with discussion and a rejoinder by Liu and Singh) , 1999 .

[25]  Mark K. Chang,et al.  Network reliability and the factoring theorem , 1983, Networks.

[26]  S. Mangan,et al.  Structure and function of the feed-forward loop network motif , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[27]  Marvin Rausand,et al.  System Reliability Theory: Models, Statistical Methods, and Applications , 2003 .

[28]  S. Shen-Orr,et al.  Network motifs: simple building blocks of complex networks. , 2002, Science.

[29]  Albert-László Barabási,et al.  Error and attack tolerance of complex networks , 2000, Nature.

[30]  R. Serfling,et al.  General notions of statistical depth function , 2000 .

[31]  Regina Y. Liu,et al.  New Nonparametric Tests of Multivariate Locations and Scales Using Data Depth , 2004 .

[32]  Martí Rosas-Casals,et al.  Robustness of the European power grids under intentional attack. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Martin Rohden,et al.  Cascading Failures in AC Electricity Grids , 2016, Physical review. E.

[34]  Subir Ghosh,et al.  Reliability and Risk: A Bayesian Perspective , 2008, Technometrics.

[35]  J. Lawless.  Statistical Models and Methods for Lifetime Data , 2002 .

[36]  Narayanaswamy Balakrishnan,et al.  Parametric inference for component distributions from lifetimes of systems with dependent components , 2012 .

[37]  Regina Y. Liu,et al.  A Quality Index Based on Data Depth and Multivariate Rank Tests , 1993 .

[38]  Jonas Johansson,et al.  Topological Performance Measures as Surrogates for Physical Flow Models for Risk and Vulnerability Analysis for Electric Power Systems , 2013, Risk analysis : an official publication of the Society for Risk Analysis.

[39]  Emilio Barocio,et al.  Vulnerability Analysis of Power Grids Using Modified Centrality Measures , 2013 .

[40]  F. Coolen,et al.  Generalizing the signature to systems with multiple types of components , 2013, SOCO 2013.

[41]  Thomas E. Gorochowski,et al.  Organization of feed-forward loop motifs reveals architectural principles in natural and engineered networks , 2017, Science Advances.

[42]  Kon Shing Kenneth Chung,et al.  Measuring topological robustness of networks under sustained targeted attacks , 2012, 2012 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining.

[43]  Jürgen Kurths,et al.  Detours around basin stability in power networks , 2014 .

[44]  Charles Kim,et al.  Vulnerability Assessment of Power Grid Using Graph Topological Indices , 2007 .

[45]  Hans J. Herrmann,et al.  Mitigation of malicious attacks on networks , 2011, Proceedings of the National Academy of Sciences.

[46]  Charles J. Colbourn,et al.  Roots of the Reliability Polynomial , 1992, SIAM J. Discret. Math..

[47]  Cohen,et al.  Resilience of the internet to random breakdowns , 2000, Physical review letters.

[48]  Reza Akbarinia,et al.  A highly scalable parallel algorithm for maximally informative k-itemset mining , 2016, Knowledge and Information Systems.

[49]  Francisco J. Samaniego,et al.  The Signature of a Coherent System and Its Applications in Reliability , 2004 .