dodgr flows In dodgr: Distances on Directed Graphs

```library (dodgr)
```

The `dodgr`package includes three functions for allocating and aggregating flows throughout network, based on defined properties of a set of origin and destination points. The three primary functions for flows are `dodgr_flows_aggregate()`, `dodgr_flows_disperse()`, and `dodgr_flows_si()`, each of which is now described in detail.

1 Flow Aggregation

The first of the above functions aggregates ''flows'' throughout a network from a set of origin (`from`) and destination (`to`) points. Flows commonly arise in origin-destination matrices used in transport studies, but may be any kind of generic flows on graphs. A flow matrix specifies the flow between each pair of origin and destination points, and the `dodgr_flows_aggregate()` function aggregates all of these flows throughout a network and assigns a resultant aggregate flow to each edge.

For a set of `nf` points of origin and `nt` points of destination, flows are defined by a simple `nf`-by-`nt` matrix of values, as in the following code:

```graph <- weight_streetnet (hampi, wt_profile = "foot")
from <- sample (graph\$from_id, size = 10)
to <- sample (graph\$to_id, size = 10)
flows <- matrix (10 * runif (length (from) * length (to)),
nrow = length (from))
```

This `flows` matrix is then submitted to `dodgr_flows_aggregate()`, which simply appends an additional column of `flows` to the submitted `graph`:

```graph_f <- dodgr_flows_aggregate (graph, from = from, to = to, flows = flows)
```

Most flows are zero because they have only been calculated between very few points in the graph.

```summary (graph_f\$flow)
```

2 Flow Dispersal

The second function, `dodgr_flows_disperse()`, uses only a vector a origin (`from`) points, and aggregates flows as they disperse throughout the network according to a simple exponential model. In place of the matrix of flows required by `dodgr_flows_aggregate()`, dispersal requires an equivalent vector of densities dispersing from all origin (`from`) points. This is illustrated in the following code, using the same graph as the previous example.

```dens <- rep (1, length (from)) # uniform densities
graph_f <- dodgr_flows_disperse (graph, from = from, dens = dens)
summary (graph_f\$flow)
```

3 Merging directed flows

Note that flows from both `dodgr_flows_aggregate()` and `dodgr_flows_disperse()` are directed, so the flow from 'A' to 'B' will not necessarily equal the flow from 'B' to 'A'. It is often desirable to aggregate flows in an undirected manner, for example for visualisations where plotting pairs of directed flows between each edge if often not feasible for large graphs. Directed flows can be aggregated to equivalent undirected flows with the `merge_directed_graph()` function:

```graph_undir <- merge_directed_graph (graph_f)
```

Resultant graphs produced by `merge_directed_graph()` only include those edges having non-zero flows, and so:

```nrow (graph_f); nrow (graph_undir) # the latter is much smaller
```

The resultant graph can readily be merged with the original graph to regain the original data on vertex coordinates through

```graph <- graph [graph_undir\$edge_id, ]
graph\$flow <- graph_undir\$flow
```

This graph may then be used to visualise flows with the `dodgr_flowmap()` function:

```graph_f <- graph_f [graph_f\$flow > 0, ]
dodgr_flowmap (graph_f, linescale = 5)
```

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dodgr documentation built on Aug. 8, 2021, 1:06 a.m.