Is that right? (From an article, Using graph theory to analyze biological networks.)
Things flow in biological systems: energy, nutrients, blood, air, as examples.
A graph is a set of points with connections.
A graph is like a photograph. Biological systems are like movies. If that analogy is valid (well, maybe it is not?), then graphs are not the optimal way to model biological system; it is necessary to also model flow.
Your views?
Before going into your answer, it is good to define the filed. I recommend to read the works of the founder and the one who could the term of complex networks:
* Regular
* Random
* Small-worlds
* Scale-free
It is actually a fascinating subject in those different classes of networks. Biological networks are often scale-free or small-world ones. Quite often are hierarchically nested in functional blocks!
The founder is Albert-Lazslo Barabasi:
https://barabasi.com/
https://www.researchgate.net/profile/Albert_Laszlo_Barabasi
I recommend you to start with some of his easy paper -- older one -- on complex networks. Alternatively, you can read his book 'networked'. It is quite a popular approach defining history, development, up to about ten years ago.
It all started with seven bridges of the Koenigsberg problem that got resolved by Euler.
Very crudely said biological networks can connect metabolic products, genes & their regulation, epigenetics, diseases and diseased genes, fluxes of any kind within cells, tissues, and bodies.
Networks are the mathematical backbone of a detailed description of processes where many different species interact among themselves but not all with each other. It is some kind of selective interactions.
I think for the beginning it is quite a big load foreveryone. Send me an answer when you dive into the subject! Mathematically, it is a really exciting field.
I think the flow of blood cant be modeled as a Graph. But we can modeled it by various parts it flows.
Energy flow can be modeled as graph but the complexity may increases because in space-time regime the energy is changing at every instance due to randomness.
I think the flow of air can also be modeled as graph. Homogeneous medium (like air) is quite complex to some extent as compared to heterogeneous medium. What happened is just because the set of data points obtained in homogeneous medium may occupy same place in the graph; as a result complexity increases while abstraction of data points from the graph.
Thank you.
Before going into your answer, it is good to define the filed. I recommend to read the works of the founder and the one who could the term of complex networks:
* Regular
* Random
* Small-worlds
* Scale-free
It is actually a fascinating subject in those different classes of networks. Biological networks are often scale-free or small-world ones. Quite often are hierarchically nested in functional blocks!
The founder is Albert-Lazslo Barabasi:
https://barabasi.com/
https://www.researchgate.net/profile/Albert_Laszlo_Barabasi
I recommend you to start with some of his easy paper -- older one -- on complex networks. Alternatively, you can read his book 'networked'. It is quite a popular approach defining history, development, up to about ten years ago.
It all started with seven bridges of the Koenigsberg problem that got resolved by Euler.
Very crudely said biological networks can connect metabolic products, genes & their regulation, epigenetics, diseases and diseased genes, fluxes of any kind within cells, tissues, and bodies.
Networks are the mathematical backbone of a detailed description of processes where many different species interact among themselves but not all with each other. It is some kind of selective interactions.
I think for the beginning it is quite a big load foreveryone. Send me an answer when you dive into the subject! Mathematically, it is a really exciting field.
Jiří Kroc
Thank you for your excellent recommendation of Barabasi's work.
In 2017, I found Barabasi's Network Science in an online version. I just checked, and it is currently still available online, I don't know if it has been updated since.
While graphs offer a way to model networks, it remains possible that there are better mathematical models grounded in entropy rather than ones based on graphs.
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