global.summary {streamDAG}

Global Summary

Description

This function calculates useful DAG global summaries including size, diameter, number of paths to sink, mean path length, mean alpha centrality, mean PageRank centrality, graph centralization, Strahler order, Shreve order, the Randic index, the first Zagreb Index, the second Zagreb index, atom-bond connectivity, the geometric-arithmatic index, the harmonic index, the Harary index, global efficiency, the assortativity correlation (+, -), and the assortativity correlation (+, +).

Usage

global.summary(G, which = "all", sink, mode = "in", inf.paths = FALSE)

Arguments

G

graph object of class "igraph". See graph_from_literal.

which

Which metric to use. Currently one of "all", "size", "diameter", "graph.order", "n.sources", "n.paths.to.sink", "sink.path.len.summary", "deg.summary", "avg.alpha.cent", "shreve.num", "strahler.num", "fst.zagreb", "scd.zagreb", "ABC", "harary", "global.efficiency", "assort.in.out", "assort.in.in".

sink

sink node from graph object G.

mode

Type of degree used. One of "in" or "out".

inf.paths

logical, consider infinite paths?

Details

Simple global graph measures of complexivity and/or connectivity of a stream DAG include size, diameter, and number of paths to a sink. The size is equal to the number of arcs in the stream network. The diameter equals the length of the longest path, i.e., the height of the sink, and in eccentricity of the sink. The number of paths to the sink is equivalent to the number of nodes from which the sink node is reachable, which will be n-1 for a fully active stream. For more information on I(D) metrics see I.D. Links describing other metrics are provided below.

Value

Returns a vector of global graph measures for G.

Author(s)

Ken Aho, Gabor Csardi wrote alpha_centrality and other underlying functions.

References

Kunkler, S. J., LaMar, M. D., Kincaid, R. K., & Phillips, D. (2013). Algorithm and complexity for a network assortativity measure. arXiv Preprint arXiv:1307.0905.

Das, K. C., Gutman, I., & Furtula, B. (2011). On atom-bond connectivity index. Chemical Physics Letters, 511(4-6), 452-454.

Li, X., & Shi, Y. (2008). A survey on the randic index. MATCH Commun. Math. Comput. Chem, 59(1), 127-156.

See Also

alpha_centrality, I.D, spath.lengths, n.sources, stream.order, harary

Examples

network_a <- graph_from_literal(a --+ b, c --+ d, d --+ e, b --+ e, 
e --+ j, j --+ m, f --+ g, g --+ i, h --+ i, i --+ k, k --+ l, 
l --+ m, m --+ n,  n --+ o)

global.summary(network_a, sink ="o")