Complex network

In the context of network theory, a complex network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in graphs modelling of real systems. The study of complex networks is a young and active area of scientific research (since 2000) inspired largely by the empirical study of real-world networks such as computer networks, technological networks, brain networks and social networks.

Definition

Most social, biological, and technological networks display substantial non-trivial topological features, with patterns of connection between their elements that are neither purely regular nor purely random. Such features include a heavy tail in the degree distribution, a high clustering coefficient, assortativity or disassortativity among vertices, community structure, and hierarchical structure. In the case of directed networks these features also include reciprocity, triad significance profile and other features. In contrast, many of the mathematical models of networks that have been studied in the past, such as lattices and random graphs, do not show these features. The most complex structures can be realized by networks with a medium number of interactions. This corresponds to the fact that the maximum information content (entropy) is obtained for medium probabilities.

Climate as complex networks

The field of Complex Networks has emerged as an important area of science to generate novel insights into nature of complex systems. The application of the theory to Climate Science is a young and emerging field. , , , To identify and analyze patterns in global climate, scientists model the climate data as Complex Networks.

Unlike most of the real-world networks in which nodes and edges are well defined, nodes in climate networks are identified with the spatial grid points of underlying global climate data set, which is defined arbitrarily and can be represented at various resolutions. Two nodes are connected by an edge depending on the degree of statistical dependence between corresponding pairs of time-series taken from climate data, on the basis of similarity shared in climatic variability.,, The climate network approach enables novel insights into the dynamics of the climate system over many spatial scales., ,

Construction of Climate Networks

Depending upon the choice of nodes and/or edges, climate networks may take many different forms, shapes, sizes and complexities. Tsonis et al introduced the field of complex networks to climate. In their model, the nodes for the network were constituted by a single variable (500 hPa) from NCEP/NCAR Reanalysis datasets. In order to estimate the edges between nodes, correlation coefficient at zero time lag between all possible pairs of nodes was estimated. A pair of nodes was considered to be connected, if their correlation coefficient is above a threshold of 0.5.