Exploring temporal (hyper)networks¶

Temporal networks contain events that happen at specific times. We construct one from a static base network and briefly look at simple reachability queries. Install the library with pip install reticula and import it:

>>> import reticula as ret

Random link activation¶

Here we use a random 4-regular graph as the base structure and activate its links according to an exponential inter-event time distribution:

>>> gen = ret.mersenne_twister(42)
>>> base = ret.random_regular_graph[ret.int64](
...     size=64, degree=4, random_state=gen)
>>> iet = ret.exponential_distribution[ret.double](lmbda=1.0)
>>> temporal = ret.random_link_activation_temporal_network(
...     base_net=base, max_t=32, iet_dist=iet, res_dist=iet,
...     random_state=gen)
>>> temporal
<undirected_temporal_network[int64, double] with 64 verts and 4026 edges>

Temporal hypergraphs¶

Using a hypergraph base works just the same. Only the edge type changes:

>>> gen = ret.mersenne_twister(42)
>>> hbase = ret.random_uniform_hypergraph[ret.int64](
...     size=100, edge_degree=3, edge_prob=0.01, random_state=gen)
>>> iet = ret.exponential_distribution[ret.double](lmbda=1.0)
>>> hyper_temporal = ret.random_link_activation_temporal_network(
...     base_net=hbase, max_t=16, iet_dist=iet, res_dist=iet,
...     random_state=gen)
>>> hyper_temporal
<undirected_temporal_hypernetwork[int64, double] with 100 verts and 26675 edges>
>>> hyper_temporal.edge_type()
<class 'undirected_temporal_hyperedge[int64, double]'>

Basic reachability¶

Simple spreading corresponds to the default temporal adjacency. The cluster of events reachable from node 0 at time 0 is obtained with out_cluster():

>>> adj = ret.temporal_adjacency.simple[temporal.edge_type()]()
>>> cluster = ret.out_cluster(temporal_network=temporal,
...     temporal_adjacency=adj, vertex=0, time=0.0)
>>> cluster.volume()
64
>>> cluster.mass()
inf
>>> cluster.lifetime()
(0.0, inf)
>>> cluster.covers(vertex=12, time=0.1)
False
>>> cluster.covers(vertex=12, time=3.1)
True

You can directly inspect the intervals where a vertex is reachable from the source of the sprading cluster:

>>> int_set = cluster.interval_sets()[12]
>>> int_set
<interval_set[double] from t=2.394805838263237 to t=inf>
>>> list(int_set)  # set of all "infected" time periods for vertex 12
[(2.394805838263237, inf)]

The same reachability functions work on this temporal hypergraph as well. For a more complex example, see the temporal network reachability example.