Quick Start#

For Python developers#

The very first step is to find a suitable development environment. Reticula is currently compatible with Linux systems based on GNU C Library 2.17 or higher, which at the moment means practically any distribution released in the past 6 years except for Alpine Linux. If you have no preferences on the subject, we recommend a long-term support (LTS) version of Ubuntu, such as 22.04.

Setting up the environment#

In this section, we will explore the most basic form of installation of Reticula. Unfortunately, the current state of Python development environment is not as intuitive as it can be, so if you are working on a computer that is administered by someone else, such a University workstation or laptop, ask your system administrators what is the best way to install a package for your specific setup.

First, open the terminal and check if you have the proper Python version installed:

$ python --version
Python 3.8.10

Acceptable values are, at the moment, 3.8, 3.9 or 3.10, though there is experimental support for PyPy 3.8 and 3.9 as well. If your Python version is not in this range, you can install proper Python version using the tools provided by your operating system.

Note

In Ubuntu and other Debian based Linux distributions, by default all Python binaries are versioned, meaning that you should be replacing all instances of python in the command line with python3.

Next, let’s make sure you have the most recent version of pip, the standard Python package-management system:

$ python -m pip install --upgrade pip

Finally, to install the Reticula package

$ python -m pip install reticula

If this command succeeds, you should be ready to go! Let’s check if everything is ready by running a one-liner script that only tries to import Reticula:

$ python -c "import reticula" && echo "success\!"
success!

Getting started with Reticula#

First, let’s open a Python console, also called a REPL:

$ python
Python 3.8.10 (default, Jun  4 2021, 15:09:15)
>>>

You can now enter Python commands one by one and have the results shown to you immediately. This is useful for testing and learning. Let’s import Reticula and try to create a network:

>>> import reticula as ret
>>> g = ret.regular_ring_lattice[ret.int64](size=100, degree=4)
>>> g
<undirected_network[int64] with 100 verts and 200 edges>

Let’s try to dissect these commands. First, we imported Reticula but instructed python to use the alias ret to refer to it. This can help you avoid having to type reticula over and over again.

Second, we called the function regular_ring_lattice[ret.int64]. This syntax might look a bit weird or unnatural to people coming from a dynamic typing background. Remember that Reticula in Python is a thin shell over C++, so some functions need more information about what type of network or edges you want to construct, especially where this is not deducible from the things you passed in as arguments. This is refelcted in the type of the output network g, which is a ret.undirected_network[ret.int64], i.e., an undirected dyadic static network with 64-bit signed integers as vertices.

Here, we instructed Reticula to construct a 4-regular ring lattice with 100 vertices, where each vertex is a 64-bit signed integer. You can compare this, for example, to the dtype parameter that many NumPy functions expect:

import numpy as np
np.array([1, 2, 3, 4], dtype=np.int64)

Let’s get back to Reticula. We can inspect the network g. Let’s have a look at the edges and vertices of g:

>>> g.edges()
[undirected_edge[int64](0, 1), undirected_edge[int64](0, 2),
undirected_edge[int64](0, 98), ..., undirected_edge[int64](98, 99)]
>>> g.vertices()
[0, 1, 2, 3, 4, 5, 6, 7, ... , 99]

So, the edges of network g are also carrying the same type information as the network itself. Let’s get one of the edges and inspect that:

>>> e = list(g.edges())[0]
>>> e
undirected_edge[int64](0, 1)
>>> e.incident_verts()
[0, 1]
>>> e.vertex_type() == ret.int64
True

Generating random networks#

Let’s try using more interesting network models. Random network models, such as Erdős–Rényi model, depend on random number generators to work. Moreover, Reticula cannot safely manipulate Python objects, such as the Python standard library pseudo-random number generator random.Random, while retaining the ability to do parallel work in different threads. Reticula, therefore, provides bindings for a pseudo-random number generator that can safely be used internally.

>>> state = ret.mersenne_twister(seed=42)

The variable state now holds a pseudo-random number generator created with seed value 42. Any Reticula algorithm, when passed this state, should produce the same outcome as long as the same seed is used.

>>> state = ret.mersenne_twister(seed=42)
>>> ret.random_gnp_graph[ret.int64](n=1000, p=0.05, random_state=state)
<undirected_network[int64] with 1000 verts and 25091 edges>

>>> # on some other computer:
>>> state = ret.mersenne_twister(seed=42)
>>> ret.random_gnp_graph[ret.int64](n=1000, p=0.05, random_state=state)
<undirected_network[int64] with 1000 verts and 25091 edges>

Usually, you need to make a single pseudo-random number generator for your python script, or one per thread for multi-threaded scripts since the order of execution is not clear. The seed(s) for the random number generators can be one of the inputs to your script, making it much easier for you and other to reproduce your results.

Using the algorithms#

Let’s now use some of the algorithms. Let’s generate a thinner network and study connectivity in this static network:

>>> state = ret.mersenne_twister(seed=42)
>>> g = ret.random_gnp_graph[ret.int64](n=1000, p=0.005, random_state=state)
>>> comps = ret.connected_components(g)
>>> len(comps)
8

So this random network consists of 8 connected components. Let’s see how the component sizes are distributed, then get the largest component:

>>> ret.is_connected(g)
False
>>> [len(c) for c in comps]
[1, 1, 1, 1, 1, 1, 1, 993]
>>> lcc = max(comps, key=len)
>>> lcc
<component[int64] of 993 nodes: {999, 998, 997, 996, 995, 994, 993, 992,
991, 990, ...})>

So a component, which is just a set of vertices, also carries the same type information as all other types. We can inspect the membership in a component and turn it into a plain old Python list of numbers:

>>> 10 in lcc
True
>>> 59 in lcc
False
>>> [v for v in g.vertices() if v not in lcc]
[59, 98, 260, 669, 713, 874, 937]

Let’s now get the subgraph of g induced by the largest connected components:

>>> g2 = ret.vertex_induced_subgraph(g, lcc)
>>> g2
<undirected_network[int64] with 993 verts and 2498 edges>
>>> ret.is_connected(g2)
True

We can also check out some other properties of the network, such as its density or average degree:

>>> # Average degree:
>>> sum(g.degree(v) for v in g.vertices())/len(g.vertices())
4.996
>>> ret.density(g)
0.005001001001001001
>>> ret.is_reachable(g, 1, 3)
True
>>> ret.is_reachable(g, 1, 59)
False