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.

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>