Succinct representation of general unlabeled graphs
Discrete Applied Mathematics
Elements of information theory
Elements of information theory
Asymptotic behavior of the Lempel-Ziv parsing scheme and digital search trees
Theoretical Computer Science - Special volume on mathematical analysis of algorithms (dedicated to D. E. Knuth)
Average Case Analysis of Algorithms on Sequences
Average Case Analysis of Algorithms on Sequences
Three great challenges for half-century-old computer science
Journal of the ACM (JACM)
On the asymmetry of random regular graphs and random graphs
Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
Precise Average Redundancy Of An Idealized Arithmetic Coding
DCC '02 Proceedings of the Data Compression Conference
Towards Compressing Web Graphs
DCC '01 Proceedings of the Data Compression Conference
Structure induction by lossless graph compression
DCC '07 Proceedings of the 2007 Data Compression Conference
Compression of words over a partially commutative alphabet
IEEE Transactions on Information Theory
Structural complexity of random binary trees
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Multiscale approach for the network compression-friendly ordering
Journal of Discrete Algorithms
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F. Brooks argues in [3] there is "no theory that gives us a metric for information embodied in structure." Shannon himself alluded to it fifty years earlier in his little known 1953 paper [14]. Indeed, in the past information theory dealt mostly with "conventional data," be it textual data, image, or video data. However, databases of various sorts have come into existence in recent years for storing "unconventional data" including biological data, web data, topographical maps, and medical data. In compressing such data structures, one must consider two types of information: the information conveyed by the structure itself, and the information conveyed by the data labels implanted in the structure. In this paper, we attempt to address the former problem by studying information of graphical structures (i.e., unlabeled graphs). In particular, we consider the Erdös-Rényi graphs G(n, p) over n vertices in which edges are added randomly with probability p. We prove that the structural entropy of G(n, p) is (2n)h(p) - log n! + o(1) = (2n)h(p) - n log n + O(n), where h(p) = -p log p - (1 - p) log (1 - p) is the entropy rate of a conventional memoryless binary source. Then, we design a two-stage encoding that optimally compresses unlabeled graphs up to the first two leading terms of the structural entropy.