7,819 research outputs found
Improving information centrality of a node in complex networks by adding edges
The problem of increasing the centrality of a network node arises in many
practical applications. In this paper, we study the optimization problem of
maximizing the information centrality of a given node in a network
with nodes and edges, by creating new edges incident to . Since
is the reciprocal of the sum of resistance distance
between and all nodes, we alternatively consider the problem of minimizing
by adding new edges linked to . We show that the
objective function is monotone and supermodular. We provide a simple greedy
algorithm with an approximation factor and
running time. To speed up the computation, we also present an
algorithm to compute -approximate
resistance distance after iteratively adding edges, the
running time of which is for any
, where the notation suppresses the factors. We experimentally demonstrate the effectiveness and
efficiency of our proposed algorithms.Comment: 7 pages, 2 figures, ijcai-201
Robustness and edge addition strategy of air transport networks : a case study of 'the Belt and Road'
Air transportation is of great importance in "the Belt and Road" (the B&R) region. The achievement of the B&R initiative relies on the availability, reliability, and safety of air transport infrastructure. A fundamental step is to find the critical elements in network performance. Considering the uneven distributions of population and economy, the current literature focusing on centrality measures in unweighted networks is not sufficient in the B&R region. By differentiating power and centrality in the B&R region, our analysis leads to two conclusions: (1) Deactivating powerful nodes causes a larger decrease in efficiency than deactivating central nodes. This indicates that powerful nodes in the B&R region are more critical than central nodes for network robustness. (2) Strategically adding edges between high powerful and low powerful nodes can enhance the network's ability to exchange resources efficiently. These findings can be used to adjust government policies for air transport configuration to achieve the best network performance and the most cost effective
Coverage Centrality Maximization in Undirected Networks
Centrality metrics are among the main tools in social network analysis. Being
central for a user of a network leads to several benefits to the user: central
users are highly influential and play key roles within the network. Therefore,
the optimization problem of increasing the centrality of a network user
recently received considerable attention. Given a network and a target user
, the centrality maximization problem consists in creating new links
incident to in such a way that the centrality of is maximized,
according to some centrality metric. Most of the algorithms proposed in the
literature are based on showing that a given centrality metric is monotone and
submodular with respect to link addition. However, this property does not hold
for several shortest-path based centrality metrics if the links are undirected.
In this paper we study the centrality maximization problem in undirected
networks for one of the most important shortest-path based centrality measures,
the coverage centrality. We provide several hardness and approximation results.
We first show that the problem cannot be approximated within a factor greater
than , unless , and, under the stronger gap-ETH hypothesis, the
problem cannot be approximated within a factor better than , where
is the number of users. We then propose two greedy approximation
algorithms, and show that, by suitably combining them, we can guarantee an
approximation factor of . We experimentally compare the
solutions provided by our approximation algorithm with optimal solutions
computed by means of an exact IP formulation. We show that our algorithm
produces solutions that are very close to the optimum.Comment: Accepted to AAAI 201
Updating and downdating techniques for optimizing network communicability
The total communicability of a network (or graph) is defined as the sum of
the entries in the exponential of the adjacency matrix of the network, possibly
normalized by the number of nodes. This quantity offers a good measure of how
easily information spreads across the network, and can be useful in the design
of networks having certain desirable properties. The total communicability can
be computed quickly even for large networks using techniques based on the
Lanczos algorithm.
In this work we introduce some heuristics that can be used to add, delete, or
rewire a limited number of edges in a given sparse network so that the modified
network has a large total communicability. To this end, we introduce new edge
centrality measures which can be used to guide in the selection of edges to be
added or removed.
Moreover, we show experimentally that the total communicability provides an
effective and easily computable measure of how "well-connected" a sparse
network is.Comment: 20 pages, 9 pages Supplementary Materia
Ricci Curvature of the Internet Topology
Analysis of Internet topologies has shown that the Internet topology has
negative curvature, measured by Gromov's "thin triangle condition", which is
tightly related to core congestion and route reliability. In this work we
analyze the discrete Ricci curvature of the Internet, defined by Ollivier, Lin,
etc. Ricci curvature measures whether local distances diverge or converge. It
is a more local measure which allows us to understand the distribution of
curvatures in the network. We show by various Internet data sets that the
distribution of Ricci cuvature is spread out, suggesting the network topology
to be non-homogenous. We also show that the Ricci curvature has interesting
connections to both local measures such as node degree and clustering
coefficient, global measures such as betweenness centrality and network
connectivity, as well as auxilary attributes such as geographical distances.
These observations add to the richness of geometric structures in complex
network theory.Comment: 9 pages, 16 figures. To be appear on INFOCOM 201
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