Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scaling Behaviors of Weighted Food Webs as Energy Transportation
  Networks   Food webs can be regarded as energy transporting networks in which the weight
of each edge denotes the energy flux between two species. By investigating 21
empirical weighted food webs as energy flow networks, we found several
ubiquitous scaling behaviors. Two random variables $A_i$ and $C_i$ defined for
each vertex $i$, representing the total flux (also called vertex intensity) and
total indirect effect or energy store of $i$, were found to follow power law
distributions with the exponents $\alpha\approx 1.32$ and $\beta\approx 1.33$,
respectively. Another scaling behavior is the power law relationship, $C_i\sim
A_i^\eta$, where $\eta\approx 1.02$. This is known as the allometric scaling
power law relationship because $A_i$ can be treated as metabolism and $C_i$ as
the body mass of the sub-network rooted from the vertex $i$, according to the
algorithm presented in this paper. Finally, a simple relationship among these
power law exponents, $\eta=(\alpha-1)/(\beta-1)$, was mathematically derived
and tested by the empirical food webs.

20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin