919 research outputs found
A Bag-of-Paths Node Criticality Measure
This work compares several node (and network) criticality measures
quantifying to which extend each node is critical with respect to the
communication flow between nodes of the network, and introduces a new measure
based on the Bag-of-Paths (BoP) framework. Network disconnection simulation
experiments show that the new BoP measure outperforms all the other measures on
a sample of Erdos-Renyi and Albert-Barabasi graphs. Furthermore, a faster
(still O(n^3)), approximate, BoP criticality relying on the Sherman-Morrison
rank-one update of a matrix is introduced for tackling larger networks. This
approximate measure shows similar performances as the original, exact, one
Fully-dynamic Approximation of Betweenness Centrality
Betweenness is a well-known centrality measure that ranks the nodes of a
network according to their participation in shortest paths. Since an exact
computation is prohibitive in large networks, several approximation algorithms
have been proposed. Besides that, recent years have seen the publication of
dynamic algorithms for efficient recomputation of betweenness in evolving
networks. In previous work we proposed the first semi-dynamic algorithms that
recompute an approximation of betweenness in connected graphs after batches of
edge insertions.
In this paper we propose the first fully-dynamic approximation algorithms
(for weighted and unweighted undirected graphs that need not to be connected)
with a provable guarantee on the maximum approximation error. The transfer to
fully-dynamic and disconnected graphs implies additional algorithmic problems
that could be of independent interest. In particular, we propose a new upper
bound on the vertex diameter for weighted undirected graphs. For both weighted
and unweighted graphs, we also propose the first fully-dynamic algorithms that
keep track of such upper bound. In addition, we extend our former algorithm for
semi-dynamic BFS to batches of both edge insertions and deletions.
Using approximation, our algorithms are the first to make in-memory
computation of betweenness in fully-dynamic networks with millions of edges
feasible. Our experiments show that they can achieve substantial speedups
compared to recomputation, up to several orders of magnitude
Considerations about multistep community detection
The problem and implications of community detection in networks have raised a
huge attention, for its important applications in both natural and social
sciences. A number of algorithms has been developed to solve this problem,
addressing either speed optimization or the quality of the partitions
calculated. In this paper we propose a multi-step procedure bridging the
fastest, but less accurate algorithms (coarse clustering), with the slowest,
most effective ones (refinement). By adopting heuristic ranking of the nodes,
and classifying a fraction of them as `critical', a refinement step can be
restricted to this subset of the network, thus saving computational time.
Preliminary numerical results are discussed, showing improvement of the final
partition.Comment: 12 page
Robustness of Trans-European Gas Networks
Here we uncover the load and fault-tolerant backbones of the trans-European
gas pipeline network. Combining topological data with information on
inter-country flows, we estimate the global load of the network and its
tolerance to failures. To do this, we apply two complementary methods
generalized from the betweenness centrality and the maximum flow. We find that
the gas pipeline network has grown to satisfy a dual-purpose: on one hand, the
major pipelines are crossed by a large number of shortest paths thereby
increasing the efficiency of the network; on the other hand, a non-operational
pipeline causes only a minimal impact on network capacity, implying that the
network is error-tolerant. These findings suggest that the trans-European gas
pipeline network is robust, i.e., error tolerant to failures of high load
links.Comment: 11 pages, 8 figures (minor changes
Embedding Graphs under Centrality Constraints for Network Visualization
Visual rendering of graphs is a key task in the mapping of complex network
data. Although most graph drawing algorithms emphasize aesthetic appeal,
certain applications such as travel-time maps place more importance on
visualization of structural network properties. The present paper advocates two
graph embedding approaches with centrality considerations to comply with node
hierarchy. The problem is formulated first as one of constrained
multi-dimensional scaling (MDS), and it is solved via block coordinate descent
iterations with successive approximations and guaranteed convergence to a KKT
point. In addition, a regularization term enforcing graph smoothness is
incorporated with the goal of reducing edge crossings. A second approach
leverages the locally-linear embedding (LLE) algorithm which assumes that the
graph encodes data sampled from a low-dimensional manifold. Closed-form
solutions to the resulting centrality-constrained optimization problems are
determined yielding meaningful embeddings. Experimental results demonstrate the
efficacy of both approaches, especially for visualizing large networks on the
order of thousands of nodes.Comment: Submitted to IEEE Transactions on Visualization and Computer Graphic
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