# make_lollipop

Defined in <`stapl/containers/graph/generators/lollipop.hpp`

>

```
template<typename GraphView>
GraphView make_lollipop(size_t m,size_t n,bool bidirectional)
```

## Summary

Generate a lollipop graph.

This is the barbell graph without the right barbell.

For and , the complete graph is connected to the path . The resulting nodes are labelled for the complete graph and for the path. The 2 subgraphs are joined via the edge . If , this is merely a complete graph.

Node labels are the integers 0 to m+n-1.

This function mutates the input graph.

This graph is an extremal example in David Aldous and Jim Fill's etext on Random Walks on Graphs. ^{1}

#### Parameters

*m*: The number of nodes in the complete subgraph.

*n*: The number of nodes in the chain.

*bidirectional*: True for adding back-edges, False for forward only.

#### Returns

A view over the generated graph.

The returned view owns its underlying container.

#### Example

```
using view_type = stapl::graph_view<stapl::multidigraph<int>>;
auto v = stapl::generators::make_lollipop<view_type>(16, 1024);
```

^{1} Aldous, David and Fill, James Allen. "Reversible Markov Chains and
Random Walks on Graphs," 2002. https://www.stat.berkeley.edu/~aldous/RWG/book.html