measure_features {manynet} | R Documentation |
Measures of network topological features
Description
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 between0
if all triangles are imbalanced and1
if all triangles are balanced.
These net_*()
functions return a single numeric scalar or value.
Usage
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)
Arguments
.data |
An object of a manynet-consistent class:
|
mark |
A logical vector the length of the nodes in the network.
This can be created by, among other things, any |
membership |
A vector of partition membership. |
resolution |
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. |
method |
There are three small-world measures implemented:
|
times |
Integer of number of simulations. |
Modularity
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.
Source
{signnet}
by David Schoch
References
On core-periphery
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
On the rich-club coefficient
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
On modularity
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
On small-worldliness
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
On scale-free networks
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
On balance theory
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
See Also
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
Examples
net_core(ison_adolescents)
net_core(ison_southern_women)
net_richclub(ison_adolescents)
net_factions(ison_southern_women)
net_modularity(ison_adolescents,
node_in_partition(ison_adolescents))
net_modularity(ison_southern_women,
node_in_partition(ison_southern_women))
net_smallworld(ison_brandes)
net_smallworld(ison_southern_women)
net_scalefree(ison_adolescents)
net_scalefree(generate_scalefree(50, 1.5))
net_scalefree(create_lattice(100))
net_balance(ison_marvel_relationships)