I'm reading a study which contains the following quotation:
"in many cases there may be limits to the number of relations that any one point in the network can sustain (Scott, 1991: 77). Where this is the case, the actual number of lines possible in any graph will be limited by the number of points in the graph and therefore, all other things being equal, larger graphs will have lower densities".
Can anyone provide me with a further reference or two to back up the idea that larger networks have lower densities?
The network density is defined as the number of actual connections divided by the number of possible connections. So, if the numerator is constant, network density goes to zero with growing size. An example of a limit for neighbor count is the Dunbar number.
https://phys.org/news/2020-08-optimal-social-networks-people.html
https://www.pnas.org/content/117/31/18355
https://www.impactlab.com/2021/03/14/what-is-dunbars-number/
Article Do online social media cut through the constraints that limi...
https://www.nature.com/articles/srep06526
Article Modeling Users' Activity on Twitter Networks: Validation of ...
ResearchGate limits the number of people I can follow to 5000, so if I want to follow a new person I've got to choose and unfollow another one.
Regards,
Joachim
Clearly Jochem is right and, in geneal, if you increase the denominator keeping fixed the numeraor this is what do you expect.
As for real networks that you meet in nature this happens very often: e.g. in the case of protein molecules (being the number of between residues contact in proteins (being aminoacid residues = nodes and contacts = edges) contact network density goes down in an exponential way..But this is not a LAW ! Any network follows its own wiring pattern depending on its physiological role, thus in lattice architectures (e.g. regular orchards, regular crystal structures..) the density remains constant with increasing the number of nodes, the same happens with gene expression networks with N > 50 or in urban communication systems.
Here you will find a brief description of different architectures variously optimized for their specific tasks:
Article Organization principles of Biological Networks: an explorative study
Article The basic principles of topology-dynamics relations in netwo...
Alessandro Giuliani Thank you, this is also very helpful. I think this is why I wondered if the original quotation could be correct - regular networks like the ones you describe don't fit. So then I guess that one aspect of the analysis of naturally-occurring networks is to determine the maximum number of connections which nodes can possess?
Searching for hubs (nodes with the maximum number of connections in a real network) is one of the possible tasks in network analysis but probably still more relvant are looking for nodes with elevated 'betweeness' (nodes witha lot of shortest paths passing by) or the nodes with higher P (participation coefficient , nodes in charge of keeping together different domains).
In empirical research is very rare that you posit questions emebedding the word 'can' for the same fact a networkis naturally ccurring you are only interested in the actual number of links and of the wiring architecture of the networks you are interested into...
see for example: Article The discovery of a putative allosteric site in SARS-CoV-2 sp...
https://www.sciencedirect.com/topics/computer-science/network-density
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