2,421 research outputs found
On Large-Scale Graph Generation with Validation of Diverse Triangle Statistics at Edges and Vertices
Researchers developing implementations of distributed graph analytic
algorithms require graph generators that yield graphs sharing the challenging
characteristics of real-world graphs (small-world, scale-free, heavy-tailed
degree distribution) with efficiently calculable ground-truth solutions to the
desired output. Reproducibility for current generators used in benchmarking are
somewhat lacking in this respect due to their randomness: the output of a
desired graph analytic can only be compared to expected values and not exact
ground truth. Nonstochastic Kronecker product graphs meet these design criteria
for several graph analytics. Here we show that many flavors of triangle
participation can be cheaply calculated while generating a Kronecker product
graph. Given two medium-sized scale-free graphs with adjacency matrices and
, their Kronecker product graph has adjacency matrix . Such
graphs are highly compressible: edges are represented in memory and can be built in a distributed setting from
small data structures, making them easy to share in compressed form. Many
interesting graph calculations have worst-case complexity bounds and often these are reduced to
for Kronecker product graphs, when a Kronecker formula can be derived yielding
the sought calculation on in terms of related calculations on and .
We focus on deriving formulas for triangle participation at vertices, , a vector storing the number of triangles that every vertex is involved
in, and triangle participation at edges, , a sparse matrix storing
the number of triangles at every edge.Comment: 10 pages, 7 figures, IEEE IPDPS Graph Algorithms Building Block
An Ensemble Framework for Detecting Community Changes in Dynamic Networks
Dynamic networks, especially those representing social networks, undergo
constant evolution of their community structure over time. Nodes can migrate
between different communities, communities can split into multiple new
communities, communities can merge together, etc. In order to represent dynamic
networks with evolving communities it is essential to use a dynamic model
rather than a static one. Here we use a dynamic stochastic block model where
the underlying block model is different at different times. In order to
represent the structural changes expressed by this dynamic model the network
will be split into discrete time segments and a clustering algorithm will
assign block memberships for each segment. In this paper we show that using an
ensemble of clustering assignments accommodates for the variance in scalable
clustering algorithms and produces superior results in terms of
pairwise-precision and pairwise-recall. We also demonstrate that the dynamic
clustering produced by the ensemble can be visualized as a flowchart which
encapsulates the community evolution succinctly.Comment: 6 pages, under submission to HPEC Graph Challeng
Scalable Edge Clustering of Dynamic Graphs via Weighted Line Graphs
Timestamped relational datasets consisting of records between pairs of
entities are ubiquitous in data and network science. For applications like
peer-to-peer communication, email, social network interactions, and computer
network security, it makes sense to organize these records into groups based on
how and when they are occurring. Weighted line graphs offer a natural way to
model how records are related in such datasets but for large real-world graph
topologies the complexity of building and utilizing the line graph is
prohibitive. We present an algorithm to cluster the edges of a dynamic graph
via the associated line graph without forming it explicitly.
We outline a novel hierarchical dynamic graph edge clustering approach that
efficiently breaks massive relational datasets into small sets of edges
containing events at various timescales. This is in stark contrast to
traditional graph clustering algorithms that prioritize highly connected
community structures. Our approach relies on constructing a sufficient subgraph
of a weighted line graph and applying a hierarchical agglomerative clustering.
This work draws particular inspiration from HDBSCAN.
We present a parallel algorithm and show that it is able to break
billion-scale dynamic graphs into small sets that correlate in topology and
time. The entire clustering process for a graph with
edges takes just a few minutes of run time on 256 nodes of a distributed
compute environment. We argue how the output of the edge clustering is useful
for a multitude of data visualization and powerful machine learning tasks, both
involving the original massive dynamic graph data and/or the non-relational
metadata. Finally, we demonstrate its use on a real-world large-scale directed
dynamic graph and describe how it can be extended to dynamic hypergraphs and
graphs with unstructured data living on vertices and edges.Comment: 26 pages, 15 figure
Multilevel Aggregation Methods for Small-World Graphs with Application to Random-Walk Ranking
We describe multilevel aggregation in the specific context of using Markov chains to rank the nodes of graphs. More generally, aggregation is a graph coarsening technique that has a wide range of possible uses regarding information retrieval applications. Aggregation successfully generates efficient multilevel methods for solving nonsingular linear systems and various eigenproblems from discretized partial differential equations, which tend to involve mesh-like graphs. Our primary goal is to extend the applicability of aggregation to similar problems on small-world graphs, with a secondary goal of developing these methods for eventual applicability towards many other tasks such as using the information in the hierarchies for node clustering or pattern recognition. The nature of small-world graphs makes it difficult for many coarsening approaches to obtain useful hierarchies that have complexity on the order of the number of edges in the original graph while retaining the relevant properties of the original graph. Here, for a set of synthetic graphs with the small-world property, we show how multilevel hierarchies formed with non-overlapping strength-based aggregation have optimal or near optimal complexity. We also provide an example of how these hierarchies are employed to accelerate convergence of methods that calculate the stationary probability vector of large, sparse, irreducible, slowly-mixing Markov chains on such small-world graphs. The stationary probability vector of a Markov chain allows one to rank the nodes in a graph based on the likelihood that a long random walk visits each node. These ranking approaches have a wide range of applications including information retrieval and web ranking, performance modeling of computer and communication systems, analysis of social networks, dependability and security analysis, and analysis of biological systems
The Treatment of Recurrent Abdominal Pain in Children: A Controlled Comparison of Cognitive-Behavioral Family Intervention and Standard Pediatric Care
This study describes the results of a controlled clinical trial involving 44 7- to 14-year-old children with recurrent abdominal pain who were randomly allocated to either cognitive-behavioral family intervention (CBFI) or standard pediatric care (SPC). Both treatment conditions resulted in significant improvements on measures of pain intensity and pain behavior. However, the children receiving CBFI had a higher rate of complete elimination of pain, lower levels of relapse at 6- and 12-month follow-up, and lower levels of interference with their activities as a result of pain and parents reported a higher level of satisfaction with the treatment than children receiving SPC. After controlling for pretreatment levels of pain, children's active self-coping and mothers' caregiving strategies were significant independent predictors of pain behavior at posttreatment
A CSO Search for -CH: Detection in the Orion Bar PDR
The results of a Caltech Submillimeter Observatory (CSO) search for
-CH, first detected by Pety et al. (2012) in observations toward the
Horsehead photodissociation region (PDR), are presented. A total of 39 sources
were observed in the 1 mm window. Evidence of emission from -CH is
found in only a single source - the Orion Bar PDR region, which shows a
rotational temperature of 178(13) K and a column density of 7(2) x
cm. In the remaining sources, upper limits of ~10
cm are found. These results are discussed in the context of guiding
future observational searches for this species.Comment: 9 pages, 8 figures, 4 table
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