These functions measure certain topological features of networks:
net_core() measures the correlation between a network
and a core-periphery model with the same dimensions.
net_richclub() measures the rich-club coefficient of a network.
net_factions() measures the correlation between a network
and a component model with the same dimensions.
If no 'membership' vector is given for the data,
node_partition() is used to partition nodes into two groups.
net_modularity() measures the modularity of a network
based on nodes' membership in defined clusters.
net_smallworld() measures the small-world coefficient for one- or
two-mode networks. Small-world networks can be highly clustered and yet
have short path lengths.
net_scalefree() measures the exponent of a fitted
power-law distribution. An exponent between 2 and 3 usually indicates
a power-law distribution.
net_balance() measures the structural balance index on
the proportion of balanced triangles,
ranging between 0 if all triangles are imbalanced and
1 if all triangles are balanced.
These net_*() functions return a single numeric scalar or value.
net_core(.data, mark = NULL)
net_richclub(.data)
net_factions(.data, membership = NULL)
net_modularity(.data, membership = NULL, resolution = 1)
net_smallworld(.data, method = c("omega", "sigma", "SWI"), times = 100)
net_scalefree(.data)
net_balance(.data){signnet} by David Schoch
An object of a manynet-consistent class:
matrix (adjacency or incidence) from {base} R
edgelist, a data frame from {base} R or tibble from {tibble}
igraph, from the {igraph} package
network, from the {network} package
tbl_graph, from the {tidygraph} package
A logical vector the length of the nodes in the network.
This can be created by, among other things, any node_is_*() function.
A vector of partition membership.
A proportion indicating the resolution scale. By default 1, which returns the original definition of modularity. The higher this parameter, the more smaller communities will be privileged. The lower this parameter, the fewer larger communities are likely to be found.
There are three small-world measures implemented:
"sigma" is the original equation from Watts and Strogatz (1998), $$\frac{\frac{C}{C_r}}{\frac{L}{L_r}}$$, where \(C\) and \(L\) are the observed clustering coefficient and path length, respectively, and \(C_r\) and \(L_r\) are the averages obtained from random networks of the same dimensions and density. A \(\sigma > 1\) is considered to be small-world, but this measure is highly sensitive to network size.
"omega" (the default) is an update from Telesford et al. (2011), $$\frac{L_r}{L} - \frac{C}{C_l}$$, where \(C_l\) is the clustering coefficient for a lattice graph with the same dimensions. \(\omega\) ranges between 0 and 1, where 1 is as close to a small-world as possible.
"SWI" is an alternative proposed by Neal (2017), $$\frac{L - L_l}{L_r - L_l} \times \frac{C - C_r}{C_l - C_r}$$, where \(L_l\) is the average path length for a lattice graph with the same dimensions. \(SWI\) also ranges between 0 and 1 with the same interpretation, but where there may not be a network for which \(SWI = 1\).
Integer of number of simulations.
Modularity measures the difference between the number of ties within each community from the number of ties expected within each community in a random graph with the same degrees, and ranges between -1 and +1. Modularity scores of +1 mean that ties only appear within communities, while -1 would mean that ties only appear between communities. A score of 0 would mean that ties are half within and half between communities, as one would expect in a random graph.
Modularity faces a difficult problem known as the resolution limit
(Fortunato and Barthélemy 2007).
This problem appears when optimising modularity,
particularly with large networks or depending on the degree of interconnectedness,
can miss small clusters that 'hide' inside larger clusters.
In the extreme case, this can be where they are only connected
to the rest of the network through a single tie.
To help manage this problem, a resolution parameter is added.
Please see the argument definition for more details.
Borgatti, Stephen P., and Martin G. Everett. 2000. “Models of Core/Periphery Structures.” Social Networks 21(4):375–95. doi:10.1016/S0378-8733(99)00019-2
Zhou, Shi, and Raul J. Mondragon. 2004. "The Rich-Club Phenomenon in the Internet Topology". IEEE Communications Letters, 8(3): 180-182. doi:10.1109/lcomm.2004.823426
Newman, Mark E.J. 2006. "Modularity and community structure in networks", Proceedings of the National Academy of Sciences 103(23): 8577-8696. doi:10.1073/pnas.0601602103
Murata, Tsuyoshi. 2010. "Modularity for Bipartite Networks". In: Memon, N., Xu, J., Hicks, D., Chen, H. (eds) Data Mining for Social Network Data. Annals of Information Systems, Vol 12. Springer, Boston, MA. doi:10.1007/978-1-4419-6287-4_7
Watts, Duncan J., and Steven H. Strogatz. 1998. “Collective Dynamics of ‘Small-World’ Networks”. Nature 393(6684):440–42. doi:10.1038/30918
Telesford QK, Joyce KE, Hayasaka S, Burdette JH, Laurienti PJ. 2011. "The ubiquity of small-world networks". Brain Connectivity 1(5): 367–75. doi:10.1089/brain.2011.0038
Neal, Zachary P. 2017. "How small is it? Comparing indices of small worldliness". Network Science. 5 (1): 30–44. doi:10.1017/nws.2017.5
Barabasi, Albert-Laszlo, and Reka Albert. 1999. "Emergence of scaling in random networks", Science, 286(5439): 509-512. doi:10.1126/science.286.5439.509
Clauset, Aaron, Cosma Rohilla Shalizi, and Mark E.J. Newman. 2009. "Power-law distributions in empirical data", SIAM Review, 51(4): 661-703. doi:10.1137/070710111
Stumpf, Michael P.H., and Mason Porter. 2012. "Critical truths about power laws", Science, 335(6069): 665-666. doi:10.1126/science.1216142
Holme, Petter. 2019. "Rare and everywhere: Perspectives on scale-free networks", Nature Communications, 10(1): 1016. doi:10.1038/s41467-019-09038-8
Heider, Fritz. 1946. "Attitudes and cognitive organization". The Journal of Psychology, 21: 107-112. doi:10.1080/00223980.1946.9917275
Cartwright, D., and Frank Harary. 1956. "Structural balance: A generalization of Heider's theory". Psychological Review, 63(5): 277-293. doi:10.1037/h0046049
net_transitivity() and net_equivalency()
for how clustering is calculated
Other measures:
measure_attributes,
measure_central_between,
measure_central_close,
measure_central_degree,
measure_central_eigen,
measure_closure,
measure_cohesion,
measure_diffusion_infection,
measure_diffusion_net,
measure_diffusion_node,
measure_heterogeneity,
measure_hierarchy,
measure_holes,
measure_periods,
measure_properties,
member_diffusion
net_core(ison_adolescents)
#> [1] -0.133
net_core(ison_southern_women)
#> [1] -0.235
net_richclub(ison_adolescents)
#> [1] 0.833
net_factions(ison_southern_women)
#> [1] -0.156
net_modularity(ison_adolescents,
node_in_partition(ison_adolescents))
#> [1] -0.205
net_modularity(ison_southern_women,
node_in_partition(ison_southern_women))
#> [1] -0.456
net_smallworld(ison_brandes)
#> [1] NaN
net_smallworld(ison_southern_women)
#> [1] -0.944
net_scalefree(ison_adolescents)
#> [1] 3.69
net_scalefree(generate_scalefree(50, 1.5))
#> [1] 2.43
net_scalefree(create_lattice(100))
#> [1] 3.46
net_balance(ison_marvel_relationships)
#> [1] 0.668