edgeGenerators {grapherator}

Edge generators.

Description

Function to add edges into a graph. The following methods are implemented so far:

addEdgesComplete

Generates a simple complete graph. I.e., an edge exists between each two nodes. However, no self-loops or multi-edges are included.

addEdgesGrid

Only usefull if nodes are generated via addNodesGrid. This method generates a Manhattan-like street network.

addEdgesOnion

This method determines the nodes on the convex hull of the node cloud in the euclidean plane and adds edges between neighbour nodes. Ignoring all nodes on the hull, this process is repeated iteratively resulting in an onion like peeling topololgy. Note that the graph is not connected! In order to ensure connectivity, another edge generator must be applied in addition, e.g., addEdgesSpanningTree.

addEdgesDelauney

Edges are determined by means of a Delauney triangulation of the node coordinates in the Euclidean plane.

addEdgesWaxman

Edges are generated using the Waxman-model, i.e., the probability p_{ij} for the edge (i, j) is given by

p_{ij} = \alpha e^{-\beta d_{ij}}

, where \alpha, \beta \geq 0 are control parameters and d_{ij} is the Euclidean distance of the nodes i and j.

addEdgesSpanningTree

A minimum spanning tree is computed based on a complete random weight matrix. All edges of the spanning tree are added. If runs is greater 1, the process is repeated for runs. However, already added edges are ignored in subsequent runs. This method is particularly useful to assist probablistic methods, e.g., Waxman model, in order to generate connected graphs.

addEdgesGilbert

Use Gilbert-model to generate edges. I.e., each edge is added with probability p \in [0, 1].

addEdgesErdosRenyi

In total m \leq n(n-1)/2 edges are added at random.

Usage

addEdgesComplete(graph, ...)

addEdgesGrid(graph, ...)

addEdgesOnion(graph, ...)

addEdgesDelauney(graph, ...)

addEdgesWaxman(graph, alpha = 0.5, beta = 0.5, ...)

addEdgesGilbert(graph, p, ...)

addEdgesErdosRenyi(graph, m, ...)

addEdgesSpanningTree(graph, runs = 1L, ...)

Arguments

graph

[grapherator]
Graph.

...

[any]
Not used at the moment.

alpha

[numeric(1)]
Positive number indicating the average degree of nodes in the Waxman model. Default is 0.5.

beta

[numeric(1)]
Positive number indicating the scale between short and long edges in the Waxman model. Default is 0.5.

p

[numeric(1)]
Probability for each edge (v_i, v_j), i, j = 1, \ldots, n to be added for Gilbert graphs.

m

[integer(1)]
Number of edges to sample for Erdos-Renyi graphs. Must be at most n(n-1)/2 where n is the number of nodes of graph.

runs

[integer(1)]
Number of runs to perform by addEdgesSpanningTree. Default is 1.

Details

Currently all edge generators create symmetric edges only.

Value

[list] List with components:

adj.mat matrix

Adjacency matrix.

generator [character(1)]

String description of the generator used.

Note

These functions are not meant to be called directly. Instead, they need to be assigned to the generator argument of addEdges.