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Graphical data arises naturally in several modern applications, including butnot limited to internet graphs, social networks, genomics and proteomics. Thetypically large size of graphical data argues for the importance of designinguniversal compression methods for such data. In most applications, thegraphical data is sparse, meaning that the number of edges in the graph scalesmore slowly than $n^2$, where $n$ denotes the number of vertices. Although insome applications the number of edges scales linearly with $n$, in others thenumber of edges is much smaller than $n^2$ but appears to scale superlinearlywith $n$. We call the former sparse graphs and the latter heavy-tailed sparsegraphs. In this paper we introduce a universal lossless compression methodwhich is simultaneously applicable to both classes. We do this by employing thelocal weak convergence framework for sparse graphs and the sparse graphonframework for heavy-tailed sparse graphs.

A Universal Lossless Compression Method applicable to Sparse Graphs and Heavy-Tailed Sparse Graphs