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  • David J. Aldous (a1) and Nathan Ross


Consider the setting of sparse graphs on N vertices, where the vertices have distinct “names”, which are strings of length O(log N) from a fixed finite alphabet. For many natural probability models, the entropy grows as c N log N for some model-dependent rate constant c. The mathematical content of this paper is the (often easy) calculation of c for a variety of models, in particular for various standard random graph models adapted to this setting. Our broader purpose is to publicize this particular setting as a natural setting for future theoretical study of data compression for graphs, and (more speculatively) for discussion of unorganized versus organized complexity.



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1.Alderson, D.L. & Doyle, J.C. (2010). Contrasting views of complexity and their implications for network-centric infrastructures. Systems, Man and Cybernetics 40: 839852.
2.Aldous, D. (1991). The continuum random tree. I. Annals of Probability 19(1): 128.
3.Aldous, D. & Lyons, R. (2007). Processes on unimodular random networks. Electronic Journal of Probability 12(54): 14541508.
4.Aldous, D. & Michael Steele, J. (2004). The objective method: probabilistic combinatorial optimization and local weak convergence. Probability on Discrete Structures, Vol. 110, Encyclopaedia of Mathematical Science, Berlin: Springer, pp. 172.
5.Boldi, P. & Vigna, S. (2003). The webgraph framework I: compression techniques. In: Proceedings of the 13th International World Wide Web Conference, pp. 595601. New York: ACM Press.
6.Chierichetti, F., Kumar, R., Lattanzi, S., Mitzenmacher, M., Panconesi, A., & Raghavan, P. (2009). On compressing social networks. Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD ’09), New York, NY, USA, ACM, pp. 219228.
7.Choi, Y. & Szpankowski, W. (2012). Compression of graphical structures: Fundamental limits, algorithms, and experiments. IEEE Transaction on Information Theory 58: 620638.
8.Chung, F. & Lu, L. (2006). Complex graphs and networks, Vol. 107 CBMS Regional Conference Series in Mathematics. Published for the Conference Board of the Mathematical Sciences, Washington, DC.
9.Cover, T.M. & Thomas, J.A. (2006). Elements of Information Theory, 2nd ednHoboken, NJ, Wiley-Interscience [John Wiley & Sons].
10.Dehmer, M. & Mowshowitz, A. (2011). A history of graph entropy measures. Information Science 181(1): 5778.
11.Kang, R.J. & McDiarmid, C. (2010). The t-improper chromatic number of random graphs. Combinatorics, Probabability and Computing 19(1): 8798.
12.Kontoyiannis, I. (2003). Pattern matching and lossy data compression on random fields. IEEE Transaction on Information Theory 49(4): 10471051.
13.Orlitsky, A., Santhanam, N.P. & Zhang, J. (2004). Universal compression of memoryless sources over unknown alphabets. IEEE Transaction on Information Theory 50(7): 14691481.
14.van den Berg, J. & Kesten, H. (1985). Inequalities with applications to percolation and reliability. Journal of Applied Probability 22(3): 556569.
15.Wagner, A.B., Viswanath, P., & Kulkarni, S.R. (2011). Probability estimation in the rare-events regime. IEEE Transaction on Information Theory 57(6): 32073229.


  • David J. Aldous (a1) and Nathan Ross


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