# Social networks with Graphs.jl

Many ABM frameworks provide graph infrastructure for analysing network properties of agents. Agents.jl is no different in that aspect, we have `GraphSpace`

for when spatial structure is not important, but connections are.

What if you wish to model something a little more complex? Perhaps a school yard full of students running around (in space), interacting via some social network. This is precisely the scenario that the MASON ABM framework uses as an introductory example in their documentation.

Rather than implementing an Agents.jl⸺specific graph structure, we can interface with Graphs.jl: a high class library for managing and implementing graphs, which can be re-used to establish social networks within existing spaces.

To begin, we load in some dependencies

```
using Agents
using SimpleWeightedGraphs: SimpleWeightedDiGraph # will make social network
using SparseArrays: findnz # for social network connections
using Random: MersenneTwister # reproducibility
```

And create a very simple agent without any extra properties

```
mutable struct Student <: AbstractAgent
id::Int
pos::Tuple{Float64,Float64}
end
```

## Rules of the schoolyard

It's lunchtime, and the students are going out to play. We assume the school building is in the centre of our space, with some fences around the building. A teacher monitors the students, and makes sure they don't stray too far towards the fence. We use a `teacher_attractor`

force to simulate a teacher's attentiveness. Students head out to the schoolyard in random directions, but adhere to some social norms.

Each student has one *friend* and one *foe*. These are chosen at random in our model, so it's possible that for any pair of students, one likes the other but this feeling is not reciprocated. The bond between pairs is chosen at random between 0 and 1, with a bond of 1 being the strongest. If the bond is *friendly*, agents wish above all else to be near their *friend*. Bonds that are *unfriendly* see students moving as far away as possible from their *foe*.

## Initialising the model

```
function schoolyard(;
numStudents = 50,
teacher_attractor = 0.15,
noise = 0.1,
max_force = 1.7,
spacing = 4.0,
seed = 6998,
)
model = ABM(
Student,
ContinuousSpace((100, 100), spacing; periodic = false);
properties = Dict(
:teacher_attractor => teacher_attractor,
:noise => noise,
:buddies => SimpleWeightedDiGraph(numStudents),
:max_force => max_force,
),
rng = MersenneTwister(seed)
)
for student in 1:numStudents
# Students begin near the school building
add_agent!(model.space.extent .* 0.5 .+ Tuple(rand(model.rng, 2)) .- 0.5, model)
# Add one friend and one foe to the social network
friend = rand(model.rng, filter(s -> s != student, 1:numStudents))
add_edge!(model.buddies, student, friend, rand(model.rng))
foe = rand(model.rng, filter(s -> s != student, 1:numStudents))
add_edge!(model.buddies, student, foe, -rand(model.rng))
end
model
end
```

`schoolyard (generic function with 1 method)`

Our model contains the `buddies`

property, which is our Graphs.jl directed, weighted graph. As we can see in the loop, we choose one `friend`

and one `foe`

at random for each `student`

and assign their relationship as a weighted edge on the graph.

## Movement dynamics

```
distance(pos) = sqrt(pos[1]^2 + pos[2]^2)
scale(L, force) = (L / distance(force)) .* force
function agent_step!(student, model)
# place a teacher in the center of the yard, so we don’t go too far away
teacher = (model.space.extent .* 0.5 .- student.pos) .* model.teacher_attractor
# add a bit of randomness
noise = model.noise .* (Tuple(rand(model.rng, 2)) .- 0.5)
# Adhere to the social network
network = model.buddies.weights[student.id, :]
tidxs, tweights = findnz(network)
network_force = (0.0, 0.0)
for (widx, tidx) in enumerate(tidxs)
buddiness = tweights[widx]
force = (student.pos .- model[tidx].pos) .* buddiness
if buddiness >= 0
# The further I am from them, the more I want to go to them
if distance(force) > model.max_force # I'm far enough away
force = scale(model.max_force, force)
end
else
# The further I am away from them, the better
if distance(force) > model.max_force # I'm far enough away
force = (0.0, 0.0)
else
L = model.max_force - distance(force)
force = scale(L, force)
end
end
network_force = network_force .+ force
end
# Add all forces together to assign the students next position
new_pos = student.pos .+ noise .+ teacher .+ network_force
move_agent!(student, new_pos, model)
end
```

`agent_step! (generic function with 1 method)`

Applying the rules for movement is relatively simple. For the network specifically, we find the student's `network`

and figure out how far apart they are. We scale this by the `buddiness`

factor (how much force we should apply), then figure out if that force should be in a positive or negative direction (*friend* or *foe*?).

The `findnz`

function is something that may require some further explanation. Graphs uses sparse vectors internally to efficiently represent data. When we find the `network`

of our `student`

, we want to convert the result to a dense representation by **find**ing the **n**on-**z**ero (`findnz`

) elements.

`model = schoolyard()`

```
AgentBasedModel with 50 agents of type Student
space: continuous space with (100.0, 100.0) extent and spacing=4.0
scheduler: fastest
properties: max_force, buddies, teacher_attractor, noise
```

## Visualising the system

Now, we can watch the dynamics of the social system unfold:

```
using InteractiveDynamics
using CairoMakie
function static_preplot!(ax, model)
obj = CairoMakie.scatter!([50 50]; color = :red) # Show position of teacher
CairoMakie.hidedecorations!(ax) # hide tick labels etc.
CairoMakie.translate!(obj, 0, 0, 5) # be sure that the teacher will be above students
end
abmvideo(
"schoolyard.mp4", model, agent_step!, dummystep;
framerate = 15, frames = 40,
title = "Playgound dynamics",
static_preplot!,
)
```

`WARNING: using InteractiveDynamics.scale in module ex-schoolyard conflicts with an existing identifier.`