Discrete Embedding for Attributed Graphs

AbstractGraph edit distance has been used since 1983 to compare objects in machine learning when these objects are represented by attributed graphs instead of vectors. In these cases, the graph edit distance is usually applied to deduce a distance between attributed graphs. This distance is defined as the minimum amount of edit operations (deletion, insertion and substitution of nodes and edges) needed to transform a graph into another. Since now, it has been stated that the distance properties have to be applied [(1) non-negativity (2) symmetry (3) identity and (4) triangle inequality] to the involved edit operations in the process of computing the graph edit distance to make the graph edit distance a metric. In this paper, we show that there is no need to impose the triangle inequality in each edit operation. This is an important finding since in pattern recognition applications, the classification ratio usually maximizes in the edit operation combinations (deletion, insertion and substitution of nodes and edges) that the triangle inequality is not fulfilled.

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X-Mark: a benchmark for node-attributed community discovery algorithms

Social Network Analysis and Mining ◽

10.1007/s13278-021-00823-2 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Salvatore Citraro ◽

Giulio Rossetti

Keyword(s):

State Of The Art ◽

Graph Clustering ◽

Clustering Methods ◽

Community Discovery ◽

Attributed Graphs ◽

Node Labels ◽

Discovery Algorithms ◽

Shed Light

AbstractGrouping well-connected nodes that also result in label-homogeneous clusters is a task often known as attribute-aware community discovery. While approaching node-enriched graph clustering methods, rigorous tools need to be developed for evaluating the quality of the resulting partitions. In this work, we present X-Mark, a model that generates synthetic node-attributed graphs with planted communities. Its novelty consists in forming communities and node labels contextually while handling categorical or continuous attributive information. Moreover, we propose a comparison between attribute-aware algorithms, testing them against our benchmark. Accordingly to different classification schema from recent state-of-the-art surveys, our results suggest that X-Mark can shed light on the differences between several families of algorithms.

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Publishing Community-Preserving Attributed Social Graphs with a Differential Privacy Guarantee

Proceedings on Privacy Enhancing Technologies ◽

10.2478/popets-2020-0066 ◽

2020 ◽

Vol 2020 (4) ◽

pp. 131-152 ◽

Cited By ~ 1

Author(s):

Xihui Chen ◽

Sjouke Mauw ◽

Yunior Ramírez-Cruz

Keyword(s):

Community Structure ◽

Differential Privacy ◽

Original Graph ◽

Attributed Graph ◽

Attributed Graphs ◽

Social Graphs ◽

Private Computation ◽

Novel Method ◽

Publishing Community ◽

New Community

AbstractWe present a novel method for publishing differentially private synthetic attributed graphs. Our method allows, for the first time, to publish synthetic graphs simultaneously preserving structural properties, user attributes and the community structure of the original graph. Our proposal relies on CAGM, a new community-preserving generative model for attributed graphs. We equip CAGM with efficient methods for attributed graph sampling and parameter estimation. For the latter, we introduce differentially private computation methods, which allow us to release communitypreserving synthetic attributed social graphs with a strong formal privacy guarantee. Through comprehensive experiments, we show that our new model outperforms its most relevant counterparts in synthesising differentially private attributed social graphs that preserve the community structure of the original graph, as well as degree sequences and clustering coefficients.

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