Towards a Systematic Evaluation of Generative Network Models

Generative graph models play an important role in network science. Unlike real-world networks, they are accessible for mathematical analysis and the number of available networks is not limited. The explanatory power of results on generative models, however, heavily depends on how realistic they are. We present a framework that allows for a systematic evaluation of generative network models. It is based on the question whether real-world networks can be distinguished from generated graphs with respect to certain graph parameters.

[1]  Pierre Baldi,et al.  Assessing the accuracy of prediction algorithms for classification: an overview , 2000, Bioinform..

[2]  Sadegh Aliakbary,et al.  Classification of complex networks based on similarity of topological network features. , 2017, Chaos.

[3]  David Easley,et al.  Networks, Crowds, and Markets: The Small-World Phenomenon , 2010 .

[4]  F. Chung,et al.  The average distances in random graphs with given expected degrees , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[5]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[6]  Kristin P. Bennett,et al.  Support vector machines: hype or hallelujah? , 2000, SKDD.

[7]  Amin Vahdat,et al.  Hyperbolic Geometry of Complex Networks , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Duncan J Watts,et al.  A simple model of global cascades on random networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[10]  Tobias Friedrich,et al.  On the Diameter of Hyperbolic Random Graphs , 2015, ICALP.

[11]  Béla Bollobás,et al.  The degree sequence of a scale‐free random graph process , 2001, Random Struct. Algorithms.

[12]  Christian Staudt,et al.  NetworKit: A tool suite for large-scale complex network analysis , 2014, Network Science.

[13]  Béla Bollobás,et al.  The Diameter of a Scale-Free Random Graph , 2004, Comb..

[14]  Tina Eliassi-Rad,et al.  A Guide to Selecting a Network Similarity Method , 2014, SDM.

[15]  Nicole Eggemann,et al.  The clustering coefficient of a scale-free random graph , 2008, Discret. Appl. Math..

[16]  Tobias Friedrich,et al.  Efficient Embedding of Scale-Free Graphs in the Hyperbolic Plane , 2018, IEEE/ACM Transactions on Networking.

[17]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[18]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[19]  Luca Gugelmann,et al.  Random Hyperbolic Graphs: Degree Sequence and Clustering , 2012, ArXiv.

[20]  Senén Barro,et al.  Do we need hundreds of classifiers to solve real world classification problems? , 2014, J. Mach. Learn. Res..

[21]  F. Chung,et al.  Connected Components in Random Graphs with Given Expected Degree Sequences , 2002 .

[22]  Ryan A. Rossi,et al.  The Network Data Repository with Interactive Graph Analytics and Visualization , 2015, AAAI.