Package 'fastnet'

Title: Large-Scale Social Network Analysis
Description: We present an implementation of the algorithms required to simulate large-scale social networks and retrieve their most relevant metrics.
Authors: Nazrul Shaikh [aut, cre], Xu Dong [aut], Luis Castro [aut], Christian Llano [ctb]
Maintainer: Nazrul Shaikh <[email protected]>
License: GPL (>= 2)
Version: 0.1.3
Built: 2025-03-04 04:17:39 UTC
Source: https://github.com/networkgroupr/fastnet

Help Index

Degree Distribution

Description

Obtain the degrees for all nodes.

Usage

dist.deg(net)

Arguments

net

The input network.

Details

Obtain the degrees for all nodes.

Value

A vector.

Author(s)

Xu Dong, Nazrul Shaikh.

Examples

## Not run: 
x.dist.deg <- dist.deg(x)
summary(x.dist.deg)
## End(Not run)

Plot of the degree distribution of a network

Description

Plot the degree distribution of a network.

Usage

draw.degdist(net)

Arguments

net

The input network.

Details

Plot the degree distribution of a network.

Value

A .gif plot.

Author(s)

Xu Dong, Nazrul Shaikh.

Examples

## Not run: 
x <-  net.erdos.renyi.gnp(1000, 0.01)
draw.degdist(x)
## End(Not run)

Plot of the cumulative degree distribution of a network

Description

Plot the cumulative degree distribution of a network, with a logarithm scale.

Usage

draw.degdist.cum(net)

Arguments

net

The input network.

Details

Plot the cumulative degree distribution of a network, with a logarithm scale.

Value

A .gif plot.

Author(s)

Xu Dong, Nazrul Shaikh.

Examples

## Not run: 
x <-  net.barabasi.albert(1000, 20)
draw.degdist.cum(x)
## End(Not run)

Plot of the cumulative degree distribution of a network, with a logarithm scale

Description

Plot the cumulative degree distribution of a network, with a logarithm scale.

Usage

draw.degdist.cum.log(net)

Arguments

net

The input network.

Details

Plot the cumulative degree distribution of a network, with a logarithm scale.

Value

A .gif plot.

Author(s)

Xu Dong, Nazrul Shaikh.

Examples

## Not run: 
x <-  net.barabasi.albert(1000, 20)
draw.degdist.cum.log(x)
## End(Not run)

Plot of the degree distribution of a network, with a logarithm scale

Description

Plot the degree distribution of a network, with a logarithm scale.

Usage

draw.degdist.log(net)

Arguments

net

The input network.

Details

Plot the degree distribution of a network, with a logarithm scale.

Value

A .gif plot.

Author(s)

Xu Dong, Nazrul Shaikh.

Examples

## Not run: 
x <-  net.erdos.renyi.gnp(1000, 0.01)
draw.degdist.log(x)
## End(Not run)

Plot of a small network

Description

Plot a small network.

Usage

draw.net(net)

Arguments

net

The input network.

Details

Plot a small network.

Value

A .gif plot.

Author(s)

Xu Dong, Nazrul Shaikh.

Examples

## Not run: 
x <-  net.ring.lattice(12,4)
draw.net(x)
## End(Not run)

Adjacency Matrix to fastnet

Description

Transform an adjacency matrix to an ego-centric list form used in fastnet.

Usage

from.adjacency(adj.mat)

Arguments

adj.mat

The input adjacency matrix

Value

A list containing the nodes of the network and their respective neighbors.

Author(s)

Xu Dong, Christian Llano.

Examples

adj.mat <- matrix(c(0,1,0,0,1,0,0,0,0,0,0,1,0,0,1,0), nrow = 4, ncol = 4)
g <- from.adjacency(adj.mat)

Edgelist to fastnet

Description

Transfer an edgelist to an ego-centric list form used in fastnet.

Usage

from.edgelist(edgelist)

Arguments

edgelist

The edge list, a vector with even number of entries.

Details

The n nodes are placed on a circle and each node is connected to the nearest k neighbors.

Value

A list containing the nodes of the network and their respective neighbors.

Author(s)

Xu Dong, Christian Llano.

Examples

edgelist <- c(1, 3, 2, 3, 3, 4, 5, 6,5,7)
g <- from.edgelist(edgelist)

Transform Network from igraph to fastnet Format

Description

Transform igraph object to an ego-centric list form used in fastnet.

Usage

from.igraph(net.igraph)

Arguments

net.igraph

The input igraph object.

Details

Masked from igraph::as_adj_list.

Value

A list containing the nodes of the network and their respective neighbors.

Author(s)

Xu Dong.

Examples

## Not run: 
library("igraph")
net.igraph <- erdos.renyi.game(100,0.1)
g <- from.igraph(net.igraph)
## End(Not run)

Histogram of all degrees of a network

Description

Plot the histogram of all degrees of a network.

Usage

histo.dist(g)

Arguments

g

The input network.

Details

Plot the histogram of all degrees of a network.

Value

A .gif plot.

Author(s)

Xu Dong, Nazrul Shaikh.

Examples

## Not run: 
x <-  net.erdos.renyi.gnp(1000, 0.05)
histo.dist(x)
## End(Not run)

Global Clustering Coefficient

Description

Calculate the global clustering coefficient of a graph.

Usage

metric.cluster.global(g)

Arguments

g

The input network.

Details

The global clustering coefficient measures the ratio of (closed) triples versus the total number of all possible triples in network g. metric.cluster.global() calculates the global clustering coefficient of g.

Value

A real constant.

Author(s)

Xu Dong, Nazrul Shaikh.

References

Wasserman, Stanley, and Katherine Faust. Social network analysis: Methods and applications. Vol. 8. Cambridge university press, 1994.

Examples

## Not run: 
x <-  net.erdos.renyi.gnp(1000, 0.01)
metric.cluster.global(x)
## End(Not run)

Mean Local Clustering Coefficient

Description

Calculate the average local clustering coefficient of a graph.

Usage

metric.cluster.mean(g)

Arguments

g

The input network.

Details

The local clustering coefficient of a node is the ratio of the triangles connected to the node and the triples centered on the node.metric.cluster.mean() calculates the (estimated) average clustering coefficient for all nodes in graph g with a justified error.

Value

A real constant.

Author(s)

Xu Dong, Nazrul Shaikh.

References

Wasserman, Stanley, and Katherine Faust. Social network analysis: Methods and applications. Vol. 8. Cambridge university press, 1994.

Examples

## Not run: 
x <-  net.erdos.renyi.gnp(n = 1000, ncores = 3, p =  0.06)
metric.cluster.mean(x) 
## End(Not run)

Median Local Clustering Coefficient

Description

Calculate the median local clustering coefficient of a graph.

Usage

metric.cluster.median(g)

Arguments

g

The input network.

Details

The local clustering coefficient of a node is the ratio of the triangles connected to the node and the triples centered on the node.metric.cluster.median() calculates the (estimated) median clustering coefficient for all nodes in graph g with a justified error.

Value

A real constant.

Author(s)

Xu Dong, Nazrul Shaikh.

References

Wasserman, Stanley, and Katherine Faust. Social network analysis: Methods and applications. Vol. 8. Cambridge university press, 1994.

Examples

## Not run: 
x <-  net.erdos.renyi.gnp(1000, 0.1)
metric.cluster.median(x)
## End(Not run)

Effective Degree

Description

Calculate the effective degree of a network.

Usage

metric.degree.effective(g, effective_rate = 0.9)

Arguments

g

The input network.
effective_rate

The effective rate (0.9 is set by default).

Details

The effective degree

Value

A real constant.

Author(s)

Xu Dong, Nazrul Shaikh.

Examples

## Not run: 
metric.degree.effective(x)
## End(Not run)

Degree Entropy

Description

Calculate the degree entropy of a graph.

Usage

metric.degree.entropy(g)

Arguments

g

The input network.

Details

Calculates the degree entropy of graph g, i.e.

Entropy(g)=−∑i=1ni∗log⁡2(i)Entropy(g) = - \sum_{i=1}^{n} i*\log _2(i)

Value

A real constant.

Author(s)

Xu Dong, Nazrul Shaikh.

References

Anand, Kartik, and Ginestra Bianconi. "Entropy measures for networks: Toward an information theory of complex topologies." Physical Review E 80, no. 4 (2009): 045102.

Examples

## Not run: 
x <-  net.erdos.renyi.gnp(1000, 0.01)
metric.degree.entropy(x)
## End(Not run)

Maximal Degree

Description

Calculate the maximal degree of a graph.

Usage

metric.degree.max(g)

Arguments

g

The input network.

Details

The maximal degree.

Value

A real constant.

Author(s)

Xu Dong, Nazrul Shaikh.

Examples

## Not run: 
metric.degree.max(x)
## End(Not run)

Efficient Maximal Degree

Description

Calculate the efficient maximal degree of a graph.

Usage

metric.degree.max.efficient(g)

Arguments

g

The input network.

Details

The efficient maximal degree is the 90

Value

A real constant.

Author(s)

Xu Dong, Nazrul Shaikh.

Examples

## Not run: x <-  net.erdos.renyi.gnp(1000, 0.01)
metric.degree.max.efficient(x)
## End(Not run)

Mean Degree

Description

Calculate the mean degree of a graph.

Usage

metric.degree.mean(g)

Arguments

g

The input network.

Details

The mean degree is the average value of the degrees of all nodes in graph g.

Value

A real constant.

Author(s)

Xu Dong, Nazrul Shaikh.

Examples

## Not run: 
x <-  net.erdos.renyi.gnp(1000, 0.01)
metric.degree.mean(x)

## End(Not run)

Median Degree

Description

Calculate the median degree of a graph.

Usage

metric.degree.median(g)

Arguments

g

The input network.

Details

The median degree is the median value of the degrees of all nodes in graph g.

Value

A real constant.

Author(s)

Xu Dong, Nazrul Shaikh.

Examples

## Not run: 
x <-  net.erdos.renyi.gnp(1000, 0.01)
metric.degree.median(x)
## End(Not run)

Minimal Degree

Description

Calculate the minimal degree of a network.

Usage

metric.degree.min(g)

Arguments

g

The input network.

Details

The minimal degree.

Value

A real constant.

Author(s)

Xu Dong, Nazrul Shaikh.

Examples

## Not run: 
metric.degree.min(x)
## End(Not run)

Standard Deviation of Degree Distribution

Description

Calculate the standard deviation of all degrees of a network.

Usage

metric.degree.sd(g)

Arguments

g

The input network.

Details

The standard deviation of all degrees of a network.

Value

A real constant.

Author(s)

Xu Dong, Nazrul Shaikh.

Examples

## Not run: 
metric.degree.sd(x)
## End(Not run)

Average Path Length

Description

Calculate the average path length of a graph.

Usage

metric.distance.apl(Network, probability = 0.95, error = 0.03,
  Cores = detectCores(), full.apl = FALSE)

Arguments

Network

The input network.
probability

The confidence level probability.
error

The sampling error.
Cores

Number of cores to use in the computations. By default uses parallel function detecCores().
full.apl

It will calculate the sampling version by default. If it is set to true, the population APL will be calculated and the rest of the parameters will be ignored.

Details

The average path length (APL) is the average shortest path lengths of all pairs of nodes in graph Network. metric.distance.apl calculates the population APL and estimated APL of graph g with a sampling error set by the user.

The calculation uses a parallel load balancing approach, distributing jobs equally among the cores defined by the user.

Value

A real value.

Author(s)

Luis Castro, Nazrul Shaikh.

References

E. W. Dijkstra. 1959. A note on two problems in connexion with graphs. Numer. Math. 1, 1 (December 1959), 269-271.

Castro L, Shaikh N. Estimation of Average Path Lengths of Social Networks via Random Node Pair Sampling. Department of Industrial Engineering, University of Miami. 2016.

Examples

## Not run: 
##Default function
x <-  net.erdos.renyi.gnp(1000,0.01)
metric.distance.apl(x)
##Population APL
metric.distance.apl(x, full.apl=TRUE)
##Sampling at 99% level with an error of 10% using 5 cores
metric.distance.apl(Network = x, probability=0.99, error=0.1, Cores=5)

## End(Not run)

Diameter

Description

Calculate the diameter of a graph.

Usage

metric.distance.diameter(Network, probability = 0.95, error = 0.03,
  Cores = detectCores(), full = TRUE)

Arguments

Network

The input network.
probability

The confidence level probability
error

The sampling error
Cores

Number of cores to use in the computations. By default uses parallel function detecCores().
full

It will calculate the popular full version by default. If it is set to FALSE, the estimated diameter will be calculated.

Details

The diameter is the largest shortest path lengths of all pairs of nodes in graph Network.

metric.distance.diameter calculates the (estimated) diameter of graph Network with a justified error.

Value

A real value.

Author(s)

Luis Castro, Nazrul Shaikh.

References

E. W. Dijkstra. 1959. A note on two problems in connexion with graphs. Numer. Math. 1, 1 (December 1959), 269-271.

Castro L, Shaikh N. Estimation of Average Path Lengths of Social Networks via Random Node Pair Sampling. Department of Industrial Engineering, University of Miami. 2016.

Examples

## Not run: 
##Default function
x <-  net.erdos.renyi.gnp(1000,0.01)
metric.distance.diameter(x)
##Population APL
metric.distance.diameter(x, full=TRUE)
##Sampling at 99% level with an error of 10% using 5 cores
metric.distance.diameter(Network = x, probability=0.99, error=0.1, Cores=5)

## End(Not run)

Effective Diameter

Description

Calculate the effective diameter of a graph.

Usage

metric.distance.effdia(Network, probability = 0.95, error = 0.03,
  effective_rate = 0.9, Cores = detectCores(), full = TRUE)

Arguments

Network

The input network.
probability

The confidence level probability
error

The sampling error
effective_rate

The effective rate (by default it is set to be 0.9)
Cores

Number of cores to use in the computations. By default uses parallel function detecCores().
full

It will calculate the popular full version by default. If it is set to FALSE, the estimated diameter will be calculated.

Details

The diameter is the largest shortest path lengths of all pairs of nodes in graph Network. metric.distance.diameter calculates the (estimated) diameter of graph Network with a justified error.

Value

A real value.

Author(s)

Luis Castro, Nazrul Shaikh.

References

Dijkstra EW. A note on two problems in connexion with graphs:(numerische mathematik, _1 (1959), p 269-271). 1959.

Castro L, Shaikh N. Estimation of Average Path Lengths of Social Networks via Random Node Pair Sampling. Department of Industrial Engineering, University of Miami. 2016.

Examples

## Not run: 
##Default function
x <-  net.erdos.renyi.gnp(1000,0.01)
metric.distance.effdia(x)
##Population APL
metric.distance.effdia(x, full=TRUE)
##Sampling at 99% level with an error of 10% using 5 cores
metric.distance.effdia(Network = x, probability=0.99, error=0.1, Cores=5)

## End(Not run)

Mean Eccentricity

Description

Calculate the mean eccentricity of a graph.

Usage

metric.distance.meanecc(g, p)

Arguments

g

The input network.
p

The sampling probability.

Details

The mean eccentricities of all nodes in graph g. Calculates the (estimated) mean eccentricity of graph g with a justified error.

Value

A real constant.

Author(s)

Xu Dong, Nazrul Shaikh.

References

West, Douglas Brent. Introduction to graph theory. Vol. 2. Upper Saddle River: Prentice Hall, 2001.

Examples

## Not run: 
x <-  net.erdos.renyi.gnp(1000, 0.01)
metric.distance.meanecc(x, 0.01)
## End(Not run)

Median Eccentricity

Description

Calculate the (estimated) median eccentricity of a graph.

Usage

metric.distance.medianecc(g, p)

Arguments

g

The input network.
p

The sampling probability.

Details

Is the median eccentricities of all nodes in graph g. metric.distance.medianecc calculates the (estimated) median eccentricity of graph g with a justified error.

Value

A real constant.

Author(s)

Xu Dong, Nazrul Shaikh.

References

West, Douglas Brent. Introduction to graph theory. Vol. 2. Upper Saddle River: Prentice hall, 2001.

Examples

## Not run: 
x <-  net.erdos.renyi.gnp(1000, 0.01)
metric.distance.medianecc(x, 0.01)
## End(Not run)

Median Path Length

Description

Calculate the median path length (MPL) of a network.

Usage

metric.distance.mpl(Network, probability = 0.95, error = 0.03,
  Cores = detectCores(), full = FALSE)

Arguments

Network

The input network.
probability

The confidence level probability
error

The sampling error
Cores

Number of cores to use in the computations. By default detecCores() from parallel.
full

It calculates the sampling version by default. If it is set to true, the population MPL will be calculated and the rest of the parameters will be ignored.

Details

The median path length (MPL) is the median shortest path lengths of all pairs of nodes in Network. metric.distance.mpl(g) calculates the population MPL OR estimated MPL of network g with a sampling error set by the user. The calculation uses a parallel load balancing approach, distributing jobs equally among the cores defined by the user.

Value

A real integer

Author(s)

Luis Castro, Nazrul Shaikh.

References

E. W. Dijkstra. 1959. A note on two problems in connexion with graphs. Numer. Math. 1, 1 (December 1959), 269-271.

Castro L, Shaikh N. Estimation of Average Path Lengths of Social Networks via Random Node Pair Sampling. Department of Industrial Engineering, University of Miami. 2016.

Examples

## Not run: 
##Default function
x <-  net.erdos.renyi.gnp(1000,0.01)
metric.distance.mpl(x)
##Population MPL
metric.distance.mpl(x, full=TRUE)
##Sampling at 99% level with an error of 10% using 5 cores
metric.distance.mpl(Network = x, probability=0.99, error=0.1, Cores=5)

## End(Not run)

Mean Eigenvalue Centrality

Description

Calculate the mean eigenvalue centrality of a graph.

Usage

metric.eigen.mean(g)

Arguments

g

The input network.

Details

metric.eigen.mean calculates the mean eigenvalue centrality score of graph g.

Value

A real constant.

Author(s)

Xu Dong, Nazrul Shaikh.

References

Bonacich, Phillip, and Paulette Lloyd. "Eigenvector-like measures of centrality for asymmetric relations." Social networks 23, no. 3 (2001): 191-201.

Borgatti, Stephen P. "Centrality and network flow." Social networks 27, no. 1 (2005): 55-71.

Examples

## Not run: 
x <-  net.erdos.renyi.gnp(1000, 0.01)
metric.eigen.mean(x)
## End(Not run)

Median Eigenvalue Centrality

Description

Calculate the median eigenvalue centrality of a graph.

Usage

metric.eigen.median(g)

Arguments

g

The input network.

Details

metric.eigen.median calculates the median eigenvalue centrality score of graph g.

Value

A real constant.

Author(s)

Xu Dong, Nazrul Shaikh.

References

Bonacich, Phillip, and Paulette Lloyd. "Eigenvector-like measures of centrality for asymmetric relations." Social networks 23, no. 3 (2001): 191-201.

Borgatti, Stephen P. "Centrality and network flow." Social networks 27, no. 1 (2005): 55-71.

Examples

## Not run: 
x <-  net.erdos.renyi.gnp(1000, 0.01)
metric.eigen.median(x)
## End(Not run)

Eigenvalue Score

Description

Calculate the eigenvalue centrality score of a graph.

Usage

metric.eigen.value(g)

Arguments

g

The input network.

Details

metric.eigen.value calculates the eigenvalue centrality score of graph g.

Value

A real constant.

Author(s)

Xu Dong, Nazrul Shaikh.

References

Bonacich, Phillip, and Paulette Lloyd. "Eigenvector-like measures of centrality for asymmetric relations." Social networks 23, no. 3 (2001): 191-201.

Borgatti, Stephen P. "Centrality and network flow." Social networks 27, no. 1 (2005): 55-71.

Examples

## Not run: 
x <-  net.erdos.renyi.gnp(1000, 0.01)
metric.eigen.value(x)
## End(Not run)

Graph Density

Description

Calculate the density of a graph.

Usage

metric.graph.density(g)

Arguments

g

The input network.

Details

Computes the ratio of the number of edges and the number of possible edges.

Value

A real constant.

Author(s)

Xu Dong, Nazrul Shaikh.

Examples

## Not run: 
x <-  net.erdos.renyi.gnp(1000, 0.01)
metric.graph.density(x)
## End(Not run)

neighbors of an agent in a network

Description

Present all neighbors of a give agent in a network.

Usage

neighbors(net, node)

Arguments

net

The input network.
node

The input node.

Details

Neighbors of a node are nodes that directly connects to this node.

Value

A vector.

Author(s)

Xu Dong, Nazrul Shaikh.

Examples

## Not run: 
x <-  net.ring.lattice(12,4)
neighbors(x,2)
## End(Not run)

Barabasi-Albert Scale-free Graph

Description

Simulate a scale-free network using a preferential attachment mechanism (Barabasi and Albert, 1999)

Usage

net.barabasi.albert(n, m, ncores = detectCores(), d = FALSE)

Arguments

n

Number of nodes of the network.
m

Number of nodes to which a new node connects at each iteration.
ncores

Number of cores, by default detectCores() from parallel.
d

A logical value determining whether the generated network is a directed or undirected (default) network.

Details

Starting with m nodes, the preferential attachment mechaism adds one node and m edges in each step. The edges will be placed with one end on the newly-added node and the other end on the existing nodes, according to probabilities that associate with their current degrees.

Value

A list containing the nodes of the network and their respective neighbors.

Author(s)

Luis Castro, Xu Dong, Nazrul Shaikh.

References

Barabasi, A.- L. and Albert R. 1999. Emergence of scaling in random networks. Science, 286 509-512.

Examples

## Not run: 
x <- net.barabasi.albert(1000, 20) # using default ncores 
## End(Not run)

Caveman Network

Description

Simulate a (connected) caveman network of m cliques of size k.

Usage

net.caveman(m, k, ncores = detectCores())

Arguments

m

Number of cliques (or caves) in the network.
k

Number of nodes per clique.
ncores

Number of cores, by default detectCores() from parallel.

Details

The (connected) caveman network is formed by connecting a set of isolated k - cliques (or "caves"), neighbor by neighbor and head to toe, using one edge that removed from each clique such that all m cliques form a single circle (Watts 1999). The total number of nodes, i.e. n, in this network is given by k∗mk*m.

Value

A list containing the nodes of the network and their respective neighbors.

Author(s)

Xu Dong, Nazrul Shaikh.

References

Watts, D. J. Networks, Dynamics, and the Small-World Phenomenon. Amer. J. Soc. 105, 493-527, 1999.

Examples

## Not run: 
x <- net.caveman(50, 20) #using ncores by default 
## End(Not run)

Complete Network

Description

Simulate a complete (or full) network.

Usage

net.complete(n, ncores = detectCores())

Arguments

n

Number of nodes of the network.
ncores

Number of cores, by default detectCores() from parallel.

Details

The n nodes in the network are fully connected.

Note that the input n should not excess 10000, for the sake of memory overflow.

Value

A list containing the nodes of the network and their respective neighbors.

Author(s)

Xu Dong, Nazrul Shaikh.

Examples

## Not run: 
x <- net.complete(1000) #using ncores by default
## End(Not run)

Directed / Undirected Erdos-Renyi G(n,m)G(n,m) network using a fix edge size.

Description

Simulate a random network with n nodes and m edges, according to Erdos and Renyi (1959).

Usage

net.erdos.renyi.gnm(n, m, ncores = detectCores(), d = TRUE)

Arguments

n

Number of nodes of the network.
m

Number of edges of the network.
ncores

Number of cores, by default detectCores() from parallel.
d

A logical value determining whether is a network directed (default) or indirected.

Details

In this (simplest) random network, m edges are formed at random among n nodes. When d = TRUE is a directed network.

Value

A list containing the nodes of the network and their respective neighbors.

Author(s)

Xu Dong, Nazrul Shaikh.

References

Erdos, P. and Renyi, A., On random graphs, Publicationes Mathematicae 6, 290-297 (1959).

Examples

## Not run: 
x <- net.erdos.renyi.gnm(1000, 100) 
## End(Not run)

Directed / Undirected Erdos-Renyi G(n,p)G(n,p) network

Description

Simulate a random network with n nodes and a link connecting probability of p, according to Edos and Renyi (1959).

Usage

net.erdos.renyi.gnp(n, p, ncores = detectCores(), d = TRUE)

Arguments

n

Number of nodes of the network.
p

Connecting probability.
ncores

Number of cores, by default detectCores() from parallel.
d

A logical value determining whether is a network directed (default) or indirected.

Details

In this (simplest) random network, each edge is formed at random with a constant probability. When d = TRUE is a directed network.

Value

A list containing the nodes of the network and their respective neighbors.

Author(s)

Luis Castro, Xu Dong, Nazrul Shaikh.

References

Erdos, P. and Renyi, A., On random graphs, Publicationes Mathematicae 6, 290-297 (1959).

Examples

## Not run: 
x <- net.erdos.renyi.gnp(1000, 0.01)
## End(Not run)

Holme-Kim Network

Description

Simulate a scale-free network with relatively high clustering, comparing to B-A networks (Holme and Kim, 1999).

Usage

net.holme.kim(n, m, pt)

Arguments

n

Number of nodes of the network.
m

Number of nodes to which a new node connects at each iteration.
pt

Triad formation probability after each preferential attachment mechanism.

Details

The Holme-Kim network model is a simple extension of B-A model. It adds an additional step, called "Triad formation", with the probability pt that compensates the low clustering in B-A networks.

Value

A list containing the nodes of the network and their respective neighbors.

Author(s)

Xu Dong, Nazrul Shaikh

References

Holme, Petter, and Beom Jun Kim. "Growing scale-free networks with tunable clustering."Physical review E65, no. 2 (2002): 026107.

Examples

## Not run: 
x <- net.holme.kim (1000, 20, 0.1)
## End(Not run)

Random Network with a Power-law Degree Distribution that Has An Exponential Cutoff

Description

Simulate a random network with a power-law degree distribution that has an exponential cutoff, according to Newman et al. (2001).

Usage

net.random.plc(n, cutoff, exponent)

Arguments

n

The number of the nodes in the network.
cutoff

Exponential cutoff of the degree distribution of the network.
exponent

Exponent of the degree distribution of the network.

Details

The generated random network has a power-law degree distribution with an exponential degree cutoff.

Value

A list containing the nodes of the network and their respective neighbors.

Author(s)

Xu Dong, Nazrul Shaikh

References

Newman, Mark EJ, Steven H. Strogatz, and Duncan J. Watts. "Random graphs with arbitrary degree distributions and their applications." Physical review E 64, no. 2 (2001): 026118.

Examples

## Not run: 
x <- net.random.plc(1000, 10, 2)
## End(Not run)

Rewired (Connected) Caveman Network

Description

Simulate a rewired caveman network of m cliques of size k, and with a link rewiring probability p.

Usage

net.rewired.caveman(nc, m, p)

Arguments

nc

Number of cliques (or caves) in the network.
m

Number of nodes per clique.
p

Link rewiring probability.

Details

The rewired caveman network is built on the corresponding regular caveman network with m cliques of size k. Then the links in this caveman network are rewired with probability p.

Value

A list containing the nodes of the network and their respective neighbors.

Author(s)

Xu Dong, Nazrul Shaikh

References

Watts, D. J. Networks, Dynamics, and the Small-World Phenomenon. Amer. J. Soc. 105, 493-527, 1999.

Examples

## Not run: 
x <- net.rewired.caveman(50, 20, 0.0005)
## End(Not run)

k - regular ring lattice

Description

Simulate a network with a k -regular ring lattice structure.

Usage

net.ring.lattice(n, k)

Arguments

n

Number of nodes in the network.
k

Number of edges per node.

Details

The n nodes are placed on a circle and each node is connected to the nearest k neighbors.

Value

A list containing the nodes of the network and their respective neighbors.

Author(s)

Xu Dong, Nazrul Shaikh

References

Duncan J Watts and Steven H Strogatz: Collective dynamics of 'small world' networks, Nature 393, 440-442, 1998.

Examples

## Not run: 
x <- net.ring.lattice(1000, 10)
## End(Not run)

Watts-Strogatz Small-world Network

Description

Simulate a small-world network according to the model of Watts and Strogatz (1998).

Usage

net.watts.strogatz(n, k, re)

Arguments

n

The number of the nodes in the network (or lattice).
k

Number of edges per node.
re

Rewiring probability.

Details

The formation of Watts-Strogatz network starts with a ring lattice with n nodes and k edges per node, then each edge is rewired at random with probability re.

Value

A list containing the nodes of the network and their respective neighbors.

Author(s)

Xu Dong, Nazrul Shaikh

References

Duncan J. Watts and Steven H. Strogatz: Collective dynamics of 'small world' networks, Nature 393, 440-442, 1998.

Examples

## Not run: 
x <- net.watts.strogatz(1000, 10, 0.05)
## End(Not run)

Preview of the degree distribution of a network

Description

Present the first 10 degrees of a network.

Usage

preview.deg(g)

Arguments

g

The input network.

Details

Present the first 10 degrees of a network.

Value

A vector.

Author(s)

Xu Dong, Nazrul Shaikh.

Examples

## Not run: 
x <-  net.ring.lattice(12,4)
preview.deg(x)
## End(Not run)

Preview of a network

Description

Present the first 10 ego-centric lists of a network.

Usage

preview.net(net)

Arguments

net

The input network.

Details

the connection condition of the first 10 nodes in a network.

Value

A list.

Author(s)

Xu Dong, Nazrul Shaikh.

Examples

## Not run: 
x <-  net.ring.lattice(12,4)
preview.net(x)
## End(Not run)