Abstract
We propose a new, recursive model to generate realistic graphs, evolving over time. Our model has the following properties: it is (a) flexible, capable of generating the cross product of weighted/unweighted, directed/undirected, uni/bipartite graphs; (b) realistic, giving graphs that obey eleven static and dynamic laws that real graphs follow (we formally prove that for several of the (power) laws and we estimate their exponents as a function of the model parameters); (c) parsimonious, requiring only four parameters. (d) fast, being linear on the number of edges; (e) simple, intuitively leading to the generation of macroscopic patterns. We empirically show that our model mimics two real-world graphs very well: Blognet (unipartite, undirected, unweighted) with 27 K nodes and 125 K edges; and Committee-to-Candidate campaign donations (bipartite, directed, weighted) with 23 K nodes and 880 K edges. We also show how to handle time so that edge/weight additions are bursty and self-similar.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Akoglu L, McGlohon M, Faloutsos C (2008) Rtm: laws and a recursive generator for weighted time-evolving graphs. In: ICDM
Albert R, Jeong H, Barabasi A-L (1999) Diameter of the world wide web. Nature 401: 130–131
Barabasi AL, Albert R (1999) Emergence of scaling in random networks. Science 286(5439): 509–512
Chakrabarti D, Faloutsos C (2006) Graph mining: laws, generators, and algorithms. ACM Comput Surv 38: 1–69
Chakrabarti D, Zhan Y, Faloutsos C (2004) R-MAT: a recursive model for graph mining. In: Fourth SIAM international conference on data mining, April 2004, Orlando, Florida, USA
Conrad B, Mitzenmacher M (2004) Power laws for monkeys typing randomly: the case of unequal probabilities. IEEE Trans Inf Theory 50(7): 1403–1414
Crovella M, Bestavros A (1996) Self-similarity in world wide web traffic, evidence and possible causes. In: Sigmetrics, pp 160–169
Erdos P, Renyi A (1960) On the evolution of random graphs. Publ Math Inst Hungary Acad Sci 5: 17–61
Even-Bar E, Kearns M, Suri S (2007) A network formation game for bipartite exchange economies. In: SODA
Fabrikant A, Luthra A, Maneva EN, Papadimitriou CH, Shenker S (2003) On a network creation game. In: PODC
Faloutsos M, Faloutsos P, Faloutsos C (1999) On power-law relationships of the internet topology. In: SIGCOMM, pp 251–262
Flake GW, Lawrence S, Giles CL, Coetzee FM (2002) Self-organization and identification of web communities. IEEE Comput 35: 66–71
Girvan M, Newman MEJ (2002) Community structure in social and biological networks. PNAS 99: 7821
Gomez ME, Santonja V (1998) Self-similarity in i/o workload: analysis and modeling. In: WWC
Gribble SD, Manku GS, Roselli D, Brewer EA, Gibson TJ, Miller EL (1998) Self-similarity in file systems. In: SIGMETRICS ’98
Kleinberg JM, Kumar R, Raghavan P, Rajagopalan S, Tomkins AS (1999) AS The Web as a graph: measurements, models and methods. In: Lecture Notes in Computer Science, vol 1627, pp 1–7
Kraetzl MSE, Nickel C (2005) Random dot product graphs: a model for social networks. In: Preliminary manuscript
Laoutaris N, Poplawski LJ, Rajaraman R, Sundaram R, Teng S-H (2008) Bounded budget connection (bbc) games or how to make friends and influence people, on a budget. In: PODC
Leskovec J, Chakrabarti D, Kleinberg JM, Faloutsos C (2005) Realistic, mathematically tractable graph generation and evolution, using Kronecker multiplication. In: PKDD, Porto, Portugal
Leskovec J, Kleinberg J, Faloutsos C (2005) Graphs over time: densification laws, shrinking diameters and possible explanations. In: ACM SIGKDD
Mandelbrot B (1953) An informational theory of the statistical structure of language. Commun Theory
McGlohon M, Akoglu L, Faloutsos C (2008) Weighted graphs and disconnected components: patterns and a generator. In: ACM SIGKDD, Las Vegas, Aug
Miller GA (1957) Some effects of intermittent silence. Am J Psychol 70: 311–314
Newman MEJ (2004) Power laws, Pareto distributions and Zipf’s law, December
Newman MEJ, Girvan M (2004) Finding and evaluating community structure in networks. Phys Rev E 69: 026113
Pennock DM, Flake GW, Lawrence S, Glover EJ, Giles CL (2002) Winners donć6t take all: characterizing the competition for links on the web. In: Proceedings of the national academy of sciences, pp 5207–5211
Schwartz MF, Wood DCM (1992) Discovering shared interests among people using graph analysis of global electronic mail traffic. Commun ACM 36: 78–89
Siganos G, Faloutsos M, Faloutsos P, Faloutsos C (2003) Power laws and the AS—level internet topology
Tsourakakis CE (2008) Fast counting of triangles in large real networks without counting: algorithms and laws. In: ICDM
Wang M, Madhyastha T, Chan NH, Papadimitriou S, Faloutsos C (2002) Data mining meets performance evaluation: fast algorithms for modeling bursty traffic. In: ICDE, pp 507–516
Watts DJ, Strogatz SH (1998) Collective dynamics of ’small-world’ networks. Nature 393(6684): 440–442
Young SJ, Scheinerman ER (2007) Random dot product graph models for social networks. In: WAW, pp 138–149
Zipf GK (1932) Selective studies and the principle of relative frequency in language. Harvard University Press
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Akoglu, L., Faloutsos, C. RTG: a recursive realistic graph generator using random typing. Data Min Knowl Disc 19, 194–209 (2009). https://doi.org/10.1007/s10618-009-0140-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10618-009-0140-7