Title: What Is the Difference between a Social and a Hyperlink Network? -- How the Type of Network Can Be Determined from the Network Structure Alone
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Networks represent a type of dataset that is ubiquitous in many disciplines and areas. Examples are social networks (ties between people), communication networks, trophic networks ("who eats who"), the World Wide Web, computer networks, lexical networks (connections between words), transport networks, metabolic networks (e.g., interactions between proteins), neural networks, animal networks, citation networks, affiliation networks (of people in groups), software dependency networks, and many more. In this talk, we present ongoing work on answering the question "Can the type of network be detected from the network structure alone?" For instance, given a completely unlabeled network dataset consisting only of node and edges, can we detect whether the data represents a social network or a hyperlink network? We present machine learning and statistical approaches to answering questions of this type. The presented results will make use of data in the KONECT project, one of the largest repositories of network datasets, curated at the University of Namur.
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Title: What Is the Difference between a Social and a Hyperlink Network? -- How the Type of Network Can Be Determined from the Network Structure Alone
- 1. naXys – Namur Centre for Complex Networks – Univ. of Namur What Is the Difference between a Social and a Hyperlink Network? How the Type of Network Can Be Determined from the Network Structure Alone Jérôme KUNEGIS University of Oxford, Department of Statistics, 2017-09-12
- 2. “Network Category” 2J. Kunegis Network Analysis
- 3. “Network Category” 3J. Kunegis Networks Are Everywhere Cliché: “Everything is a Network” It's a cliché because it's true: – Social network, road network, lexical network, metabolic network, trophic network, affiliation network, citation network, hyperlink network, etc., etc., etc.
- 4. “Network Category” 4J. Kunegis Network Categories From https://github.com/kunegis/konect-handbook
- 5. “Network Category” 5J. Kunegis Collections of Network Datasets SNAP – by Jure Leskovec, Stanford Univ. (~2009) – several 100 networks; not systematic – Available for download – Some statistics available KONECT – by Jérôme Kunegis, Univ. of Namur (~2011) – 1000+ networks, but only 200+ unipartite – Most networks available for download – Many statistics available ICON – by Aaron Clauset, Univ. of Colorado (~2016) – 4000+ datasets – Not available for download (“index”)
- 6. “Network Category” 6J. Kunegis Datasets in KONECT In this work: 165 non-bipartite networks (out of 194 non-bip. networks in KONECT)
- 7. “Network Category” 7J. Kunegis Network Statistics A statistic is a real number that characterizes a network Examples: – Average degree (d) – Number of triangles (t) – Diameter (δ) – Clustering coefficient (c) – Gini coefficient of degree distribution (G) – Degree assortativity (ρ)
- 8. “Network Category” 8J. Kunegis More Statistics – Number of wegdes (s) – Number of squares (q) – Number of claws (z) – Number of crosses (x) – Maximum degree (dmax) – Relative maximum degree (dMR = dmax / d) – Number of degree-1 nodes (d )₁ – 50-percentile effective diameter (δ0.5) – Relative edge distribution entropy (Her) – Bipartivity (bA = 1 – λmin[A] / λmax[A]) – Normalized two-star count (sd = s / (n d (d – 1) / 2)) – Eigenvalues of certain matrices (a = λ2[L], |λmax[A]|, …) – etc.
- 9. “Network Category” 9J. Kunegis Distribution of Clustering Coefficient (c) Communication Interaction Hyperlink Online social
- 10. “Network Category” 10J. Kunegis Distribution of Gini Coefficient (G) Online social Infrastructure Interaction Hum an social
- 11. “Network Category” 11J. Kunegis Distribution of Diameter (δ) Infrastructure Hyperlink Citation
- 12. “Network Category” 12J. Kunegis Degree Assortativity (ρ)
- 13. “Network Category” 13J. Kunegis Statistical Testing Kolmogorov–Smirnov test on each pair of categories; non-white cell when statistic is significantly different (p < 0.10). Base colour by HSL: Hue denotes network statistic; S & L is constant. Shown colour is interpolated between base colour and white for 0 ≤ p ≤ 0.10. Statistics (fixed position):
- 14. “Network Category” 14J. Kunegis Statistics Are Not Uncorrelated
- 15. “Network Category” 15J. Kunegis Principal Component Analysis of Statistics
- 16. “Network Category” 16J. Kunegis PCA of Network Datasets
- 17. “Network Category” 17J. Kunegis Feature Engineering Find size-independent formulations of statistics – E.g., c instead of t Avoid highly correlated statistics – E.g., keep only one of G and P Find statistics that are easy to compute – E.g., algebraic connectivity (a) needs O(n²) runtime
- 18. “Network Category” 18J. Kunegis Thank You What We Want: – More datasets, in particular, more diverse categories! – More statistics: both ideas, and code Contribute – konect.math.fundp.ac.be (temporary URL!) – Ask me about Stu: our build tool for doing all of this https://github.com/kunegis/konecttoolbox https://github.com/kunegis/konectanalysis https://github.com/kunegis/konectextr https://github.com/kunegis/konecthandbook https://github.com/kunegis/konectwww https://github.com/kunegis/stu For more news about KONECT: follow @KONECTproject Jérôme Kunegis <jerome.kunegis@unamur.be>