Volume 107, Number 5, September 2014
|Number of page(s)||6|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||04 September 2014|
Node-weighted measures for complex networks with directed and weighted edges for studying continental moisture recycling
1 Potsdam Institute for Climate Impact Research - P.O. Box 60 12 03, 14412 Potsdam, Germany, EU
2 Department of Geography, Humboldt University - Newtonstr. 15, 12489 Berlin, Germany, EU
3 Department of Physics, Humboldt University - Newtonstr. 15, 12489 Berlin, Germany, EU
4 Department of Control Theory, Nizhny Novgorod State University - Gagarin Avenue 23, 606950 Nizhny Novgorod, Russia
5 Stockholm Resilience Centre, Stockholm University - Kräftriket 2B, 114 19 Stockholm, Sweden, EU
Received: 28 April 2014
Accepted: 12 August 2014
In many real-world networks nodes represent agents or objects of different sizes or importance. However, the size of the nodes is rarely taken into account in network analysis, possibly inducing bias in network measures and confusion in their interpretation. Recently, a new axiomatic scheme of node-weighted network measures has been suggested for networks with undirected and unweighted edges. However, many real-world systems are best represented by complex networks which have directed and/or weighted edges. Here, we extend this approach and suggest new versions of the degree and the clustering coefficient associated to network motifs for networks with directed and/or weighted edges and weighted nodes. We apply these measures to a spatially embedded network model and a real-world moisture recycling network. We show that these measures improve the representation of the underlying systems' structure and are of general use for studying any type of complex network.
PACS: 89.75.-k – Complex systems / 89.75.Hc – Networks and genealogical trees / 92.60.Kc – Land/atmosphere interactions
© EPLA, 2014
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