11,063 research outputs found
A Faster Method to Estimate Closeness Centrality Ranking
Closeness centrality is one way of measuring how central a node is in the
given network. The closeness centrality measure assigns a centrality value to
each node based on its accessibility to the whole network. In real life
applications, we are mainly interested in ranking nodes based on their
centrality values. The classical method to compute the rank of a node first
computes the closeness centrality of all nodes and then compares them to get
its rank. Its time complexity is , where represents total
number of nodes, and represents total number of edges in the network. In
the present work, we propose a heuristic method to fast estimate the closeness
rank of a node in time complexity, where . We
also propose an extended improved method using uniform sampling technique. This
method better estimates the rank and it has the time complexity , where . This is an excellent improvement over the
classical centrality ranking method. The efficiency of the proposed methods is
verified on real world scale-free social networks using absolute and weighted
error functions
Reliability of rank order in sampled networks
In complex scale-free networks, ranking the individual nodes based upon their
importance has useful applications, such as the identification of hubs for
epidemic control, or bottlenecks for controlling traffic congestion. However,
in most real situations, only limited sub-structures of entire networks are
available, and therefore the reliability of the order relationships in sampled
networks requires investigation. With a set of randomly sampled nodes from the
underlying original networks, we rank individual nodes by three centrality
measures: degree, betweenness, and closeness. The higher-ranking nodes from the
sampled networks provide a relatively better characterisation of their ranks in
the original networks than the lower-ranking nodes. A closeness-based order
relationship is more reliable than any other quantity, due to the global nature
of the closeness measure. In addition, we show that if access to hubs is
limited during the sampling process, an increase in the sampling fraction can
in fact decrease the sampling accuracy. Finally, an estimation method for
assessing sampling accuracy is suggested
Using network centrality measures to manage landscape connectivity
We use a graph-theoretical landscape modeling approach to investigate how to identify central patches in the landscape as well as how these central patches influence (1) organism movement within the local neighborhood, and (2) the dispersal of organisms beyond the local neighborhood. Organism movements were theoretically estimated based on the spatial configuration of the habitat patches in the studied landscape. We find that centrality depends on the way the graph-theoretical model of habitat patches is constructed, although even the simplest network representation, not taking strength and directionality of potential organisms flows into account, still provides a coarse-grained assessment of the most important patches according to their contribution to landscape connectivity. Moreover, we identify (at least) two general classes of centrality. One accounts for the local flow of organisms in the neighborhood of a patch and the other for the ability to maintain connectivity beyond the scale of the local neighborhood. Finally, we study how habitat patches with high scores on different network centrality measures are distributed in a fragmented agricultural landscape in Madagascar. Results show that patches with high degree-, and betweenness centrality are widely spread, while patches with high subgraph- and closeness centrality are clumped together in dense clusters. This finding may enable multi-species analyses of single-species network models
- âŠ