29 research outputs found
Locally Estimating Core Numbers
Graphs are a powerful way to model interactions and relationships in data
from a wide variety of application domains. In this setting, entities
represented by vertices at the "center" of the graph are often more important
than those associated with vertices on the "fringes". For example, central
nodes tend to be more critical in the spread of information or disease and play
an important role in clustering/community formation. Identifying such "core"
vertices has recently received additional attention in the context of {\em
network experiments}, which analyze the response when a random subset of
vertices are exposed to a treatment (e.g. inoculation, free product samples,
etc). Specifically, the likelihood of having many central vertices in any
exposure subset can have a significant impact on the experiment.
We focus on using -cores and core numbers to measure the extent to which a
vertex is central in a graph. Existing algorithms for computing the core number
of a vertex require the entire graph as input, an unrealistic scenario in many
real world applications. Moreover, in the context of network experiments, the
subgraph induced by the treated vertices is only known in a probabilistic
sense. We introduce a new method for estimating the core number based only on
the properties of the graph within a region of radius around the
vertex, and prove an asymptotic error bound of our estimator on random graphs.
Further, we empirically validate the accuracy of our estimator for small values
of on a representative corpus of real data sets. Finally, we evaluate
the impact of improved local estimation on an open problem in network
experimentation posed by Ugander et al.Comment: Main paper body is identical to previous version (ICDM version).
Appendix with additional data sets and enlarged figures has been added to the
en
Efficient Truss Maintenance in Evolving Networks
Truss was proposed to study social network data represented by graphs. A
k-truss of a graph is a cohesive subgraph, in which each edge is contained in
at least k-2 triangles within the subgraph. While truss has been demonstrated
as superior to model the close relationship in social networks and efficient
algorithms for finding trusses have been extensively studied, very little
attention has been paid to truss maintenance. However, most social networks are
evolving networks. It may be infeasible to recompute trusses from scratch from
time to time in order to find the up-to-date -trusses in the evolving
networks. In this paper, we discuss how to maintain trusses in a graph with
dynamic updates. We first discuss a set of properties on maintaining trusses,
then propose algorithms on maintaining trusses on edge deletions and
insertions, finally, we discuss truss index maintenance. We test the proposed
techniques on real datasets. The experiment results show the promise of our
work
A Fast Order-Based Approach for Core Maintenance
Graphs have been widely used in many applications such as social networks,
collaboration networks, and biological networks. One important graph analytics
is to explore cohesive subgraphs in a large graph. Among several cohesive
subgraphs studied, k-core is one that can be computed in linear time for a
static graph. Since graphs are evolving in real applications, in this paper, we
study core maintenance which is to reduce the computational cost to compute
k-cores for a graph when graphs are updated from time to time dynamically. We
identify drawbacks of the existing efficient algorithm, which needs a large
search space to find the vertices that need to be updated, and has high
overhead to maintain the index built, when a graph is updated. We propose a new
order-based approach to maintain an order, called k-order, among vertices,
while a graph is updated. Our new algorithm can significantly outperform the
state-of-the-art algorithm up to 3 orders of magnitude for the 11 large real
graphs tested. We report our findings in this paper
Incremental Maintenance of Maximal Cliques in a Dynamic Graph
We consider the maintenance of the set of all maximal cliques in a dynamic
graph that is changing through the addition or deletion of edges. We present
nearly tight bounds on the magnitude of change in the set of maximal cliques,
as well as the first change-sensitive algorithms for clique maintenance, whose
runtime is proportional to the magnitude of the change in the set of maximal
cliques. We present experimental results showing these algorithms are efficient
in practice and are faster than prior work by two to three orders of magnitude.Comment: 18 pages, 8 figure
K-Connected Cores Computation in Large Dual Networks
© 2018, The Author(s). Computing k- cores is a fundamental and important graph problem, which can be applied in many areas, such as community detection, network visualization, and network topology analysis. Due to the complex relationship between different entities, dual graph widely exists in the applications. A dual graph contains a physical graph and a conceptual graph, both of which have the same vertex set. Given that there exist no previous studies on the k- core in dual graphs, we formulate a k-connected core (k- CCO) model in dual graphs. A k- CCO is a k- core in the conceptual graph, and also connected in the physical graph. Given a dual graph and an integer k, we propose a polynomial time algorithm for computing all k- CCOs. We also propose three algorithms for computing all maximum-connected cores (MCCO), which are the existing k- CCOs such that a (k+ 1) -CCO does not exist. We further study a subgraph search problem, which is computing a k- CCO that contains a set of query vertices. We propose an index-based approach to efficiently answer the query for any given parameter k. We conduct extensive experiments on six real-world datasets and four synthetic datasets. The experimental results demonstrate the effectiveness and efficiency of our proposed algorithms
Core Decomposition in Multilayer Networks: Theory, Algorithms, and Applications
Multilayer networks are a powerful paradigm to model complex systems, where
multiple relations occur between the same entities. Despite the keen interest
in a variety of tasks, algorithms, and analyses in this type of network, the
problem of extracting dense subgraphs has remained largely unexplored so far.
In this work we study the problem of core decomposition of a multilayer
network. The multilayer context is much challenging as no total order exists
among multilayer cores; rather, they form a lattice whose size is exponential
in the number of layers. In this setting we devise three algorithms which
differ in the way they visit the core lattice and in their pruning techniques.
We then move a step forward and study the problem of extracting the
inner-most (also known as maximal) cores, i.e., the cores that are not
dominated by any other core in terms of their core index in all the layers.
Inner-most cores are typically orders of magnitude less than all the cores.
Motivated by this, we devise an algorithm that effectively exploits the
maximality property and extracts inner-most cores directly, without first
computing a complete decomposition.
Finally, we showcase the multilayer core-decomposition tool in a variety of
scenarios and problems. We start by considering the problem of densest-subgraph
extraction in multilayer networks. We introduce a definition of multilayer
densest subgraph that trades-off between high density and number of layers in
which the high density holds, and exploit multilayer core decomposition to
approximate this problem with quality guarantees. As further applications, we
show how to utilize multilayer core decomposition to speed-up the extraction of
frequent cross-graph quasi-cliques and to generalize the community-search
problem to the multilayer setting
Mining (maximal) span-cores from temporal networks
When analyzing temporal networks, a fundamental task is the identification of
dense structures (i.e., groups of vertices that exhibit a large number of
links), together with their temporal span (i.e., the period of time for which
the high density holds). We tackle this task by introducing a notion of
temporal core decomposition where each core is associated with its span: we
call such cores span-cores.
As the total number of time intervals is quadratic in the size of the
temporal domain under analysis, the total number of span-cores is quadratic
in as well. Our first contribution is an algorithm that, by exploiting
containment properties among span-cores, computes all the span-cores
efficiently. Then, we focus on the problem of finding only the maximal
span-cores, i.e., span-cores that are not dominated by any other span-core by
both the coreness property and the span. We devise a very efficient algorithm
that exploits theoretical findings on the maximality condition to directly
compute the maximal ones without computing all span-cores.
Experimentation on several real-world temporal networks confirms the
efficiency and scalability of our methods. Applications on temporal networks,
gathered by a proximity-sensing infrastructure recording face-to-face
interactions in schools, highlight the relevance of the notion of (maximal)
span-core in analyzing social dynamics and detecting/correcting anomalies in
the data