R: Compute local scan statistics on graphs

local_scan {igraph} | R Documentation

## Compute local scan statistics on graphs

### Description

The scan statistic is a summary of the locality statistics that is computed from the local neighborhood of each vertex. The `local_scan` function computes the local statistics for each vertex for a given neighborhood size and the statistic function.

### Usage

    local_scan(graph.us, graph.them = NULL, k = 1, FUN = NULL,
      weighted = FALSE, mode = c("out", "in", "all"), neighborhoods = NULL,
      ...)

### Arguments

`graph.us, graph` | An igraph object, the graph for which the scan statistics will be computed
`graph.them` | An igraph object or `NULL`, if not `NULL`, then the ‘them’ statistics is computed, i.e. the neighborhoods calculated from `graph.us` are evaluated on `graph.them`.
`k` | An integer scalar, the size of the local neighborhood for each vertex. Should be non-negative.
`FUN` | Character, a function name, or a function object itself, for computing the local statistic in each neighborhood. If `NULL`(the default value), `ecount` is used for unweighted graphs (if `weighted=FALSE`) and a function that computes the sum of edge weights is used for weighted graphs (if `weighted=TRUE`). This argument is ignored if `k` is zero.
`weighted` | Logical scalar, TRUE if the edge weights should be used for computation of the scan statistic. If TRUE, the graph should be weighted. Note that this argument is ignored if `FUN` is not `NULL`, `"ecount"` and `"sumweights"`.
`mode` | Character scalar, the kind of neighborhoods to use for the calculation. One of ‘`out`’, ‘`in`’, ‘`all`’ or ‘`total`’. This argument is ignored for undirected graphs.
`neighborhoods` | A list of neighborhoods, one for each vertex, or `NULL`. If it is not `NULL`, then the function is evaluated on the induced subgraphs specified by these neighborhoods. In theory this could be useful if the same `graph.us` graph is used for multiple `graph.them` arguments. Then the neighborhoods can be calculated on `graph.us` and used with multiple graphs. In practice, this is currently slower than simply using `graph.them` multiple times.
`...` | Arguments passed to `FUN`, the function that computes the local statistics.

### Details

See the given reference below for the details on the local scan statistics.

`local_scan` calculates exact local scan statistics.

If `graph.them` is `NULL`, then `local_scan` computes the ‘us’ variant of the scan statistics. Otherwise, `graph.them` should be an igraph object and the ‘them’ variant is computed using `graph.us` to extract the neighborhood information, and applying `FUN` on these neighborhoods in `graph.them`.

### Value

For `local_scan` typically a numeric vector containing the computed local statistics for each vertex. In general a list or vector of objects, as returned by `FUN`.

### References

Priebe, C. E., Conroy, J. M., Marchette, D. J., Park, Y. (2005). Scan Statistics on Enron Graphs. Computational and Mathematical Organization Theory.

### See Also

Other scan statistics: `scan_stat`

### Examples

    pair <- sample_correlated_gnp_pair(n = 10^3, corr = 0.8, p = 0.1)
    local_0_us <- local_scan(graph.us = pair$graph1, k = 0)
    local_1_us <- local_scan(graph.us = pair$graph1, k = 1)

    local_0_them <- local_scan(graph.us = pair$graph1,
                               graph.them = pair$graph2, k = 0)
    local_1_them <- local_scan(graph.us = pair$graph1,
                               graph.them = pair$graph2, k = 1)

    Neigh_1 <- neighborhood(pair$graph1, order = 1)
    local_1_them_nhood <- local_scan(graph.us = pair$graph1,
                                     graph.them = pair$graph2,
                                     neighborhoods = Neigh_1)

[Package igraph version 1.2.2 Index]