31,492 research outputs found
A Degeneracy Framework for Scalable Graph Autoencoders
In this paper, we present a general framework to scale graph autoencoders
(AE) and graph variational autoencoders (VAE). This framework leverages graph
degeneracy concepts to train models only from a dense subset of nodes instead
of using the entire graph. Together with a simple yet effective propagation
mechanism, our approach significantly improves scalability and training speed
while preserving performance. We evaluate and discuss our method on several
variants of existing graph AE and VAE, providing the first application of these
models to large graphs with up to millions of nodes and edges. We achieve
empirically competitive results w.r.t. several popular scalable node embedding
methods, which emphasizes the relevance of pursuing further research towards
more scalable graph AE and VAE.Comment: International Joint Conference on Artificial Intelligence (IJCAI
2019
On Strong Diameter Padded Decompositions
Given a weighted graph G=(V,E,w), a partition of V is Delta-bounded if the diameter of each cluster is bounded by Delta. A distribution over Delta-bounded partitions is a beta-padded decomposition if every ball of radius gamma Delta is contained in a single cluster with probability at least e^{-beta * gamma}. The weak diameter of a cluster C is measured w.r.t. distances in G, while the strong diameter is measured w.r.t. distances in the induced graph G[C]. The decomposition is weak/strong according to the diameter guarantee.
Formerly, it was proven that K_r free graphs admit weak decompositions with padding parameter O(r), while for strong decompositions only O(r^2) padding parameter was known. Furthermore, for the case of a graph G, for which the induced shortest path metric d_G has doubling dimension ddim, a weak O(ddim)-padded decomposition was constructed, which is also known to be tight. For the case of strong diameter, nothing was known.
We construct strong O(r)-padded decompositions for K_r free graphs, matching the state of the art for weak decompositions. Similarly, for graphs with doubling dimension ddim we construct a strong O(ddim)-padded decomposition, which is also tight. We use this decomposition to construct (O(ddim),O~(ddim))-sparse cover scheme for such graphs. Our new decompositions and cover have implications to approximating unique games, the construction of light and sparse spanners, and for path reporting distance oracles
Flow-based Influence Graph Visual Summarization
Visually mining a large influence graph is appealing yet challenging. People
are amazed by pictures of newscasting graph on Twitter, engaged by hidden
citation networks in academics, nevertheless often troubled by the unpleasant
readability of the underlying visualization. Existing summarization methods
enhance the graph visualization with blocked views, but have adverse effect on
the latent influence structure. How can we visually summarize a large graph to
maximize influence flows? In particular, how can we illustrate the impact of an
individual node through the summarization? Can we maintain the appealing graph
metaphor while preserving both the overall influence pattern and fine
readability?
To answer these questions, we first formally define the influence graph
summarization problem. Second, we propose an end-to-end framework to solve the
new problem. Our method can not only highlight the flow-based influence
patterns in the visual summarization, but also inherently support rich graph
attributes. Last, we present a theoretic analysis and report our experiment
results. Both evidences demonstrate that our framework can effectively
approximate the proposed influence graph summarization objective while
outperforming previous methods in a typical scenario of visually mining
academic citation networks.Comment: to appear in IEEE International Conference on Data Mining (ICDM),
Shen Zhen, China, December 201
Detection of the elite structure in a virtual multiplex social system by means of a generalized -core
Elites are subgroups of individuals within a society that have the ability
and means to influence, lead, govern, and shape societies. Members of elites
are often well connected individuals, which enables them to impose their
influence to many and to quickly gather, process, and spread information. Here
we argue that elites are not only composed of highly connected individuals, but
also of intermediaries connecting hubs to form a cohesive and structured
elite-subgroup at the core of a social network. For this purpose we present a
generalization of the -core algorithm that allows to identify a social core
that is composed of well-connected hubs together with their `connectors'. We
show the validity of the idea in the framework of a virtual world defined by a
massive multiplayer online game, on which we have complete information of
various social networks. Exploiting this multiplex structure, we find that the
hubs of the generalized -core identify those individuals that are high
social performers in terms of a series of indicators that are available in the
game. In addition, using a combined strategy which involves the generalized
-core and the recently introduced -core, the elites of the different
'nations' present in the game are perfectly identified as modules of the
generalized -core. Interesting sudden shifts in the composition of the elite
cores are observed at deep levels. We show that elite detection with the
traditional -core is not possible in a reliable way. The proposed method
might be useful in a series of more general applications, such as community
detection.Comment: 13 figures, 3 tables, 19 pages. Accepted for publication in PLoS ON
Truss Decomposition in Massive Networks
The k-truss is a type of cohesive subgraphs proposed recently for the study
of networks. While the problem of computing most cohesive subgraphs is NP-hard,
there exists a polynomial time algorithm for computing k-truss. Compared with
k-core which is also efficient to compute, k-truss represents the "core" of a
k-core that keeps the key information of, while filtering out less important
information from, the k-core. However, existing algorithms for computing
k-truss are inefficient for handling today's massive networks. We first improve
the existing in-memory algorithm for computing k-truss in networks of moderate
size. Then, we propose two I/O-efficient algorithms to handle massive networks
that cannot fit in main memory. Our experiments on real datasets verify the
efficiency of our algorithms and the value of k-truss.Comment: VLDB201
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