14,968 research outputs found
Detecting Blackholes and Volcanoes in Directed Networks
In this paper, we formulate a novel problem for finding blackhole and volcano
patterns in a large directed graph. Specifically, a blackhole pattern is a
group which is made of a set of nodes in a way such that there are only inlinks
to this group from the rest nodes in the graph. In contrast, a volcano pattern
is a group which only has outlinks to the rest nodes in the graph. Both
patterns can be observed in real world. For instance, in a trading network, a
blackhole pattern may represent a group of traders who are manipulating the
market. In the paper, we first prove that the blackhole mining problem is a
dual problem of finding volcanoes. Therefore, we focus on finding the blackhole
patterns. Along this line, we design two pruning schemes to guide the blackhole
finding process. In the first pruning scheme, we strategically prune the search
space based on a set of pattern-size-independent pruning rules and develop an
iBlackhole algorithm. The second pruning scheme follows a divide-and-conquer
strategy to further exploit the pruning results from the first pruning scheme.
Indeed, a target directed graphs can be divided into several disconnected
subgraphs by the first pruning scheme, and thus the blackhole finding can be
conducted in each disconnected subgraph rather than in a large graph. Based on
these two pruning schemes, we also develop an iBlackhole-DC algorithm. Finally,
experimental results on real-world data show that the iBlackhole-DC algorithm
can be several orders of magnitude faster than the iBlackhole algorithm, which
has a huge computational advantage over a brute-force method.Comment: 18 page
Graph Symmetry Detection and Canonical Labeling: Differences and Synergies
Symmetries of combinatorial objects are known to complicate search
algorithms, but such obstacles can often be removed by detecting symmetries
early and discarding symmetric subproblems. Canonical labeling of combinatorial
objects facilitates easy equivalence checking through quick matching. All
existing canonical labeling software also finds symmetries, but the fastest
symmetry-finding software does not perform canonical labeling. In this work, we
contrast the two problems and dissect typical algorithms to identify their
similarities and differences. We then develop a novel approach to canonical
labeling where symmetries are found first and then used to speed up the
canonical labeling algorithms. Empirical results show that this approach
outperforms state-of-the-art canonical labelers.Comment: 15 pages, 10 figures, 1 table, Turing-10
An efficient and principled method for detecting communities in networks
A fundamental problem in the analysis of network data is the detection of
network communities, groups of densely interconnected nodes, which may be
overlapping or disjoint. Here we describe a method for finding overlapping
communities based on a principled statistical approach using generative network
models. We show how the method can be implemented using a fast, closed-form
expectation-maximization algorithm that allows us to analyze networks of
millions of nodes in reasonable running times. We test the method both on
real-world networks and on synthetic benchmarks and find that it gives results
competitive with previous methods. We also show that the same approach can be
used to extract nonoverlapping community divisions via a relaxation method, and
demonstrate that the algorithm is competitively fast and accurate for the
nonoverlapping problem.Comment: 14 pages, 5 figures, 1 tabl
- …