When we have to represent or model these social networks, in mathematics, informatics,or in digital science,
the first object we want to use, the first type of model is in fact graphs, to grasp the social network's structure.
So in a graph, there are hubs which represent people for example, and there are arcs that represent the connection between these people.
From that, we can quickly observe this graph model can become more interesting,
and different types of graphs represent different types of social networks.
For instance, if in a social network I can have several connections with a person: a family and a professional one
then we'll go from a graph to a multigraph, that is to say we can establish several arcs between these two same hubs.
For example, if I'm interested in networks in which relations are oriented like in Twitter. the relation in Twitter If i follow someone but that person doesn't need to follow me, so the relation has one direction I'll therefore use orientated graphs.
Whereas for Facebook,I don't need one because the relation, by default, is symmetrical
so I don't need to orientate my graph.
I'll also be led to look if there are different types of connections in my network,
on LinkedIn for example, I can have a professional connection or any other kind, so we'll concentrate on graph types we call "labelled", that is to say we'll put the different types of connections on the graph's arcs. And so on...
Graphs are an example amongst others, we can also be interested in representing communities,
the aim isn't to study the structure of the social network but to look at the groups inside,
for example, people with common interests. And even from a mathematical viewpoint, with graphs, we could use other structures such as matrices.
A matrix can be built from a graph, particularly what we call an adjacency matrix, that is to say, that for each arc in my graph, for each connection in my social network, I'll put a little 1 to show there's a relation.
For example, if I take a adjacency matrix, columns and lines all have my network's hubs, and if there's a link between 2 hubs in my network,
I'll indicate it in the box at the intersection point of the matching column and line, to show there's a small arc, I'll put a 1.
It can also change in time, for example, if I'm interested in networks in which you put weights, that's to say to represent the certainty or the strength of a relation between 2 people,
I'll use what we call a weighted graph, in a symmetrical way I'll have an adjacency matrix, where instead of putting 1s in the matrix, I'll put small weights to show how strong the relation is.
According to the different types of networks, I'll have to use different types of models, and according to the different treatments I want to execute.
So there are many scientific and technical stakes with social networks, which we've just seen on with the models. This is already a scientific question, which model can I choose to represent and store this social network data?
How can this model be implemented in an efficient way so that it takes the least space as possible, and is indexed as efficiently as can be, to enable access in the most efficient way?
But also, how can I distribute it on several machines when it gets too big and can't fit on one machine? So the question of the model, its representation, storing and data management raise scientific and technical questions.
further on, in informatics, there are always 2 aspects, data structures and algorithms, and so the question about the way we treat the data also raises.
In this case, treatments can be very complex So, they are difficult in two ways,
first, because we can have big volumes of data: now social networks have billions of relations inside, so because of the size, then the treatment itself will be complicated, here's an example.
A rather common treatment in a social network is the find the shortest way between two people, to see how they are connected.
And so, to look for this shortest way is already a treatment that can take time as all the links should be studied, amongst them, check which ones link the hubs we are interested in, and then the smallest one has to be chosen, that's already complicated.
Furthermore, in social networks, we are interested in finding the most central people in the network for example, to see who the most influential people in the network are.
To do so, there's an indicator called betweenness centrality, and so when this indicator is calculated, it checks how many times a person is on the shortest way between two other hubs, in other words, we check how intermediary it is, how they are crossed to connect others.
We can see we are going to have to calculate other shortest ways for each hub to see which ones often appear on the shortest ways. We can see that the complexity increases again.
So if we put together the fact that we have big volumes of data and the fact that calculations are complex, we can see that it will lead to calculation optimisation questions, and even calculation estimations to have results that are not precise, but good enough and early enough.
Many other questions arise from a technological point of view, for example, these graphs will probably change with time, social networks change, relations are created or removed,
so how will deal with these changes?
How do we represent them?
How do we analyse them?
As many questions about the graph's temporality, or will these graphs exchange content?
We spoke about social media, so we communicate not only with text but pictures, sound, etc. How do we treat these contents? How can we analyse them?
Regarding social networks, we look at the structure to have indicators, to know who's interested in which social network subject, for example. These questions are in close relation to technologies and digital science,but there are many other questions.
It's a multidisciplinary issue in fact since there are legal stakes. Through these social networks, there are political stakes and societal stakes.
So we could say that it's precisely because these networks are social networks that they raise multidisciplinary issues and all disciplines are questioned.