Understanding Complex Systems: When BigData meets Network ScienceIngo Scholtes

Abstract: Better understanding and controlling complex systems has become a grandchallenge not only for computer science, but also for the natural and social sciences.Many of these systems have in common that they can be studied from a networkperspective. Consequently methods from network science have proven instrumental intheir analysis. In this article, I introduce the macroscopic perspective that is at the heartof network science. Summarizing my recent research activities, I discuss how acombination of this perspective with Big Data methods can improve our understandingof complex systems.

ACM CCS: Networks → Network properties → Network structure; Networks →Network properties → Network dynamics; Software and its engineering → Collaborationin software development; Computing methodologies → Machine learning approaches

Keywords: complex networks, data mining, socio-technical systems, temporal networks

1 Complex Systems: A Network Perspective

We live in a connected world, with complex networkedsystems all around us. Examples include globally distri-buted information systems like the World Wide Web,the increasingly digitized social fabric into which we areembedded, as well as critical infrastructures like tele-communication networks, electrical grids or transporta-tion systems which we depend on. Better understanding,designing and controlling such systems, and preventingemerging systemic risks has become a grand challengefor computer science. Luckily, we are not alone in thisendeavour. Complex systems consisting of thousands ormillions of interconnected elements are studied in dis-ciplines as diverse as sociology, economy, managementscience, biology, neuroscience or physics. And thanks tothe ongoing trend towards computational sciences, the-se studies increasingly translate into quantitative rese-arch employing Big Data methods: Driven by the factthat social interactions increasingly manifest themselvesas digital traces, computational social science uses theresulting fine-grained data to study the structure anddynamics of social systems. Large-scale data sets cove-ring trade relations and market dynamics have resultedin a surge of data-driven modelling approaches in areassuch as Quantitative economics or Econophysics. Andthe development of high-throughput genetic sequencingand high-resolution medical imaging techniques has trig-gered an explosion of data being studied in the different

areas of computational biology.

What do these research themes have in common andwhy are they relevant for computer science? The answeris that the complex systems studied in these seeminglydifferent areas give rise to relational data which can berepresented as complex networks. Such a representationis not only useful to study how the elements of a sy-stem are connected to each other and which of thoseelements are most important. More importantly, net-work science provides us with a macroscopic perspectiveon complex systems which can be used to differentia-te structure from noise, thus providing the foundationfor pattern recognition, machine learning and statisti-cal inference techniques. As such, it is not surprisingthat network science has become instrumental for thedevelopment of statistical and computational tools thatfacilitate Big Data analyses of complex systems not onlyin computer science, but also in the natural and socialsciences [1, 2].

In this article, I introduce the macroscopic perspecti-ve which is at the heart of network science. Summari-zing recent work, I demonstrate how it can be appliedin data-driven studies of socio-technical systems. High-lighting challenges and limitations of this perspective,I finally comment on interesting current research topicsas well as on opportunities for future research.

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2 Network Science: The Macro-Perspective

How can we analyze data from networked systems? Thereader may argue that graph-theoretic methods have be-en standard techniques since the earliest days of compu-ter science. This is true, however these methods makethe important assumption that we have full knowled-ge about the network, i.e. that we precisely know towhich other nodes each node is connected. This detai-led knowledge then allows us to apply a wealth of node-and network-level measures, algorithms and visualizati-ons which can provide important insights about complexsystems. However, the condition of full knowledge aboutmicroscopic details proves difficult in many real-worldscenarios: For large decentralized systems like, e.g., theInternet or P2P systems, mapping network topologiescan be anything from costly and time-consuming to im-possible. Furthermore, as systems evolve such data arelikely to be inaccurate as soon as they have been collec-ted. And even if we succeed, we may end up with datasets comprised of Billions of nodes and hundreds of Bil-lion of links. At this scale, graph-theoretic analyses maybe possible in principle, however the time and resourcesthey demand are often prohibitive.

There is a common theme in the scenarios describedabove: We lack information about system details andare thus required to reason under uncertainty. Combi-ning methods from random graph theory and statisticalphysics, this problem can be addressed by a macroscopicperspective on networked systems, which is often subsu-med under the umbrella of network science. Notably,statistical physics faces a similar problem, being requi-red to reason about particle systems despite a lack ofknowledge about microscopic details such as particle po-sitions, velocities or interactions. Probabilistic methods,which are based on aggregate statistics of large populati-ons rather than details of individual elements, have thusbeen developed for this purpose. The same ideas can beapplied to analyze large-scale networked systems andit involves the following three steps: We first computeaggregate statistics of interest, such as the number ofnodes, the density of links, the distribution of node de-grees, the presence of clustering structures, correlationsbetween neighboring nodes, etc. Notably, using distribu-ted data processing techniques, such aggregate statisticscan be computed efficiently even for massive data sets,while for distributed systems they can be estimated effi-ciently by means of sensible sampling techniques. Basedon these statistics, in a second step we can then definestatistical ensembles, i.e. probability spaces in which weassign probabilities to all possible network realizationswhich are consistent with the given aggregate statistics.Using analytical tools like generating functions, or com-putational statistics methods like Metropolis sampling,we can finally reason about the expected properties of asystem given that we only know aggregate statistics ofits network topology.

3 Applications in Socio-technical systems

In most of the literature, the macroscopic perspectiveoutlined above is heavily associated with terminologyand methods from statistical and computational phy-sics. This can be daunting, however it should not pre-vent us from using these methods to address problemsin domains relevant to computer science. One domainin which we applied these methods is empirical softwareengineering, which is concerned with the question howcomplex software systems evolve and how humans col-laborate in their development. Here, a network scienceperspective can be applied to large-scale data coveringboth technical and social aspects of software systems.

Considering the technical dimension, we can mine soft-ware repositories to extract evolving networks of de-pendencies between software artifacts such as methods,classes or packages. We recently applied this methodto quantify the congruence between developer-declaredmodules (e.g. packages in Java) in software architectu-res and cluster patterns emerging in their dependencynetworks [3]. A high degree of congruence correspondsto a reasonable modular structure in which dependen-cies are preferentially contained within modules. Here,the macro-perspective on networks is instrumental toestablish a statistically significant measure which pro-perly accounts for the level of congruence that we canalready expect at random. The resulting measure pro-vides interesting insights into the evolution of softwarearchitectures which typically start out in a state of highmodular congruence which decreases as they grow. Itcan further be used to inform refactoring efforts thatimprove the modular structure and thus the maintaina-bility of complex software projects [3].

While this work takes a network perspective on the tech-nical dimension of software projects, it is equally import-ant to consider social aspects emerging in teams of devel-opers. How do social structures affect the performanceof development teams? Are there indicators for emer-ging problems in social organizations? And how shouldwork be organized to be most productive? Again, we canaddress these questions by a combination of large-scaledata analysis and network science methods. Using datathat cover the full history of large Open Source Softwarecommunities, we performed a statistical analysis of evol-ving networks that capture collaborations between com-munity members [4]. Here, the macroscopic perspectiveon networks allowed us to go beyond a micro-level ana-lysis of the (highly dynamic) collaboration structures.Using macroscopic and time-dependent measures whichcapture the efficiency of information flow and synchroni-zation processes, we can instead identify regime changeswhich affect the performance of development teams, aswell as the effect of a single individual leaving the pro-ject [4]. We foresee that project managers can use similarmacro-level monitoring techniques to identify emergingrisks in software projects.

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Using a macro-perspective on networks, statistical pat-terns at the aggregate level can inform us about collec-tive properties of a social organization, such as their ro-bustness or the efficiency of information flow. A differentyet related question is whether we can identify statisti-cally significant patterns which show how individualsare influenced by the network structures around them.We studied this question using data on more than 5.8Million time-stamped transactions recorded by the bugtrackers of four major Open Source Software projectsover a period of more than a decade [5]. A statisticalanalysis revealed that the position of community mem-bers in the evolving collaboration networks is a strongindicator for the quality of the bug reports they pro-vide. Addressing the question how we can improve thedesign of collaboration tools, we utilized this finding toautomatically identify valid bug reports that refer to ac-tual software defects. For this, we combined our networkperspective on collaboration structures with a machinelearning classifier, thus obtaining an automated methodthat identifies valid bug reports with a precision of upto 90.3% [5]. Notably, taking a network perspective onthe problem of identifying valid bug reports allowed usto achieve a significant improvement over previous ap-proaches addressing the same question.

Clearly, we don’t have to limit the use of these methodsto problems in empirical software engineering. The fin-ding that the position of individuals in social networksis correlated with the (perceived) quality of informati-on they provide, points to interesting general questionsthat are relevant in the design of information and re-commender systems. We thus applied our approach ofcombining machine learning and network science techni-ques to a data set of more than 100, 000 scholarly publi-cations linked by Millions of citations [6]. Studying cor-relations between citation and coauthorship networks,our results show that the citation counts of scholars de-pend in a statistically significant way on their positionin the coauthorship network. This dependence actuallyallows for an automated classifier, which - solely ba-sed on the network position of their authors - predictswith high precision which papers will be highly citedin the future. While one needs to interpret these resultscarefully, they provide interesting insights about mecha-nisms of social cognition and social information filteringat work in large social information systems [7]. They canfurther be seen as a cautionary tale, contributing to thedebate about the fallacies of citation-based informationranking mechanisms and impact measures.

4 Challenges and Research Perspectives

Without doubt, methods from network science provideinteresting opportunities for data-driven studies of com-plex systems. On the one hand, they help us to betterunderstand the complex systems that we design. On theother hand, the network perspective allows to identify

analogies to complex systems studied in other discipli-nes, thus generating insights that go beyond our ownfield. At the same time, it cannot be denied that ourunderstanding of network-based methods is still in itsinfancy, thus posing both challenges and opportunitiesfor future research.

Limitations of Ensemble Studies A first challengeresults from the interpretation of findings that are ba-sed on the macro-perspective outlined in section 2. Thisapproach helps us to derive expected properties of net-works based on aggregate statistics, which is particular-ly handy in situations where we cannot use informationabout a system’s details. However we need to be carefulwhen interpreting these expected properties. More preci-sely, the realizations subsumed in a statistical ensemblecan exhibit large variances. As such, the properties of aparticular realization observed in reality can differ qui-te substantially from the expected properties computedbased on the ensemble. This may seem trivial, howe-ver a number of works in network science have failed toclearly express this fundamental limitation of ensemblestudies, thus triggering a lively scientific debate [8].

As for any other methodology, considering the limita-tions and implicit assumptions of network science me-thods is crucial to arrive at the right conclusions. I be-lieve the best way to address this issue is by means ofbetter education. At ETH Zurich we have taken up thechallenge by developing an interdisciplinary course onnetwork science which teaches students from compu-ter science, engineering, neuroscience, management, andphysics to benefit from these methods, while being alertto their limitations.

Reasoning about Temporal Networks A secondmajor challenge is associated with the fact network to-pologies of real systems are not static, but rather changecontinuously. This may seem obvious, however it posesa problem for how we typically represent such dyna-mic systems: We mostly consider them as static net-works, aggregating all links that occur within a certaintime interval. However, with this we neglect the tempo-ral dimension of networked systems, possibly arriving atwrong conclusions about the robustness of systems, theimportance of nodes or dynamical processes [9].

Addressing the analysis of such temporal networks, muchof my latest research has focused on the question how wecan better incorporate time in network-based studies. Asimple yet important question which we studied recentlyis how the ordering of links affects causality in complexsystems. As an example, consider a simple network withthree nodes a, b, and c, connected by two time-stampedlinks (a, b, t) and (b, c, t′) at times t and t′. Clearly, nodea can only influence c, if (a, b) appears before (b, c), i.e. ift < t′. Studying data from social, biological and techni-cal systems, we showed that neglecting the order of links

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severely limits our understanding of dynamical proces-ses in networked systems [10]. To overcome these limita-tions, we developed higher-order aggregate networks, ageneralization of the commonly used static network ab-straction that allows to incorporate both the topologyand the order of links in the analysis of time-stamped re-lational data [11]. These works highlight the presence ofa largely unexplored temporal-topological dimension ofcomplex systems with interesting opportunities for newdata mining techniques which I look forward to furtherexplore in future research.

Towards Multi-Layer Network Models Finally, athird major challenge is due to the rather simplisticway in which most current network-based studies re-present data from complex systems: Elements of a sy-stem are mostly represented as featureless nodes connec-ted by a single type of links (possibly with differentstrengths). This clearly is an oversimplification of re-al systems, which often exhibit multiple types of linksor nodes with heterogeneous characteristics. Furthermo-re, for many systems such as communication networks orthe electrical grid it is non-trivial to define system boun-daries which would allow to study them in isolation.By means of mutual dependencies, engineered systemsare rather increasingly interwoven, thus requiring novelmodeling approaches which capture their multi-layeredstructure. [12]. So far, reconciling the macro-perspectiveof network science with the complex characteristics ofreal-world systems has proven to be a challenge. Howe-ver, recent advances in the theory of interconnected andmulti-layer networks can be seen as promising steps inthe direction of developing a multi-layer network science.

5 Conclusion

As networked systems affect more and more aspects ofour lives, a solid understanding of their structure anddynamics is of paramount importance. The macrosco-pic perspective on networks, along with the associatedstatistical, computational and analytical techniques pro-vide us with a rich set of tools helping us to better un-derstand, and thus design, complex systems. Analyzinglarge-scale relational data from systems occurring in na-ture and society, they further allow us to address a broadrange of scientific questions. I thus believe that the com-bination of methods from network science and Big Dataprovides an exciting and fertile field of study for a newgeneration of interdisciplinary computer scientists. I fur-ther believe that computer science is particularly adeptto provide the required combination of theoretical ex-pertise in the modeling of systems and practical skills inthe analysis of massive data sets.

Through a combination of theoretical research impro-ving network-based data-mining methods, and appliedresearch demonstrating applications in socio-technical

systems, I look forward to contribute to this excitingfield. I am further convinced that my GI Junior Fellow-ship will help me to foster the interdisciplinary exchangerequired to better understand the complex systems thatincreasingly influence our lives.

Literature

[1] M. van Steen. On the Complexity of Simple Distributed Sy-stems. IEEE Distributed Systems Online, 5(5), 2004

[2] A. Vespignani. Modelling dynamical processes in complexsocio-technical systems. Nature Physics, 8:32-39, 2012

[3] M.S. Zanetti, C.J. Tessone, I. Scholtes, F. Schweitzer. Auto-mated Software Remodularization Based on Move Refacto-ring. 13th International Conference on Modularity, 2014.

[4] M.S. Zanetti, I. Scholtes, C.J. Tessone, F. Schweitzer. Therise and fall of a central contributor: Dynamics of social or-ganization and performance in the Gentoo community. In-ternational Workshop on Cooperative and Human Aspects ofSoftware Engineering, pp. 49-56, 2013.

[5] M.S. Zanetti, I. Scholtes, C.J. Tessone, F. Schweitzer. Cate-gorizing bugs with social networks: A case study on four opensource software communities. 35th International Conferenceon Software Engineering (ICSE), pp. 1032-1041, 2013

[6] E. Sarigol, R. Pfitzner, I. Scholtes, A. Garas, F. Schweit-zer. Predicting Scientific Success Based on Coauthorship Net-works. EPJ Data Science, 3, 2014.

[7] I. Scholtes, R. Pfitzner, F. Schweitzer. The Social Dimensionof Information Ranking: A Discussion of Research Challen-ges and Approaches. Socioinformatics - The Social Impact ofInteractions between Humans and IT, Springer Proceedingsin Complexity, pp. 45-61, October 2014

[8] J.C. Doyle, D.L. Anderson, L. Li, S. Low, M. Roughan, S.Shalunov, W. Willinger. The “robust yet fragile” nature ofthe Internet. PNAS, 102(41):14497-14502, 2005.

[9] P. Holme, J. Sarimaki. Temporal networks. Physics Reports,519(3):97-125, 2012

[10] R. Pfitzner, I. Scholtes, A. Garas, C.J. Tessone, F. Schweitzer.Betweenness Preference: Quantifying Correlations in the To-pological Dynamics of Temporal Networks. Phys. Rev. Lett.,110(19):198701, 2013.

[11] I. Scholtes, N. Wider, R. Pfitzner, A. Garas, C.J. Tessone,F. Schweitzer. Causality-driven slow-down and speed-up ofdiffusion in non-Markovian temporal networks. Nature Com-munications, 5:5024, 2014.

[12] S. Tomforde, J. Hahner, B. Sick. Interwoven Systems. Infor-matik Spektrum, 37(5):483-487, 2014

Dr. Ingo Scholtes is a senior rese-archer at the Chair of Systems Designat ETH Zurich. Following studies incomputer science and mathematics, hecompleted his doctorate studies in theSystems Software and Distributed Sy-stems group at the University of Trierin 2011. He was involved in the LargeHadron Collider experiment at CERN,designing and implementing a Peer-to-Peer-based framework for large-scaledata distribution which is since beingused to monitor particle collision datafrom the ATLAS detector. Inspired by

this experience, he turned his attention to the modeling and ana-lysis of complex networked systems. His latest research addres-ses applications of network science in the analysis of data fromsocio-technical systems, but also from biology and sociology. In atheoretical line of research he further studies new methods in theanalysis of time-stamped network data. At ETH Zurich he deve-loped a course on network science which bridges the curricula ofengineering and natural sciences. He previously held a scholarshipfrom the Studienstiftung des Deutschen Volkes and was awardeda Junior-Fellowship from the Gesellschaft fur Informatik in 2014.

Address: ETH Zurich, Chair of Systems Design, CH-8092 Zurich,Switzerland, E-Mail: ischoltes@ethz.ch

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