Regular decomposition of large graphs and other structures: Scalability and robustness towards missing data

Abstract

A method for compression of large graphs and matrices to a block structure is further developed. Szemerédi's regularity lemma is used as a generic motivation of the significance of stochastic block models. Another ingredient of the method is Rissanen's minimum description length principle (MDL). We continue our previous work on the subject, considering cases of missing data and scaling of algorithms to extremely large size of graphs. In this way it would be possible to find out a large scale structure of a huge graphs of certain type using only a tiny part of graph information and obtaining a compact representation of such graphs useful in computations and visualization.

Regular Decomposition: an information and graph theoretic approach to stochastic block models

“…Bolla [3] has developed a spectral approach for finding regular structures of graphs and matrices. Our emphasis is more information-theoretical by nature and continues the works [12,15,19,20,21]. It would be very interesting to compare the methods of [24,3] and those of this paper in depth.…”

“…Remark 4.13 It is also possible to find a regular decompositions in the case of partly missing matrix elements [20,21]and also in the case of mixed positive and negative entries. In the latter case, we can use the idea of directed links already used in [12].…”

Towards analyzing large graphs with quantum annealing and quantum gate computers

“…In our previous works, we have extensively referred to SRL as a basis for graph analysis using various SBMs as a modeling space [1], [5]- [9]. Here we introduce another contact point between SBM and SRL.…”

On model selection for dense stochastic block models

“…The results are also shown to hold with Poissonian edge weights. We have applied Poissonian block models as a heuristic for finding regular structures in large real-world data matrices, in a method we call regular decomposition [11,12,15,17,18].…”