Six species are labelled and their feeding links (an edge means one species is…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Thermal, Statistical & Complex Systems · Linear algebra and vector spaces

Many Parts, One Behaviour, Ch Communities: finding the groups in a network

Problem

Six species are labelled

A,B,C,D,E,F

and their feeding links (an edge means one species is recorded eating the other) give the adjacency matrix, in that alphabetical order,

\mathbf A=\begin{pmatrix}0&1&0&1&0&1\\1&0&1&0&1&0\\0&1&0&1&0&1\\1&0&1&0&1&0\\0&1&0&1&0&1\\1&0&1&0&1&0\end{pmatrix}.

((a)) Reorder the rows and columns by placing

A,C,E

first and

B,D,F

second. Write out the reordered matrix and describe its block pattern in words (which blocks are all zero and which are dense). ((b)) Using the reordered matrix, count the number of edges lying inside each group and the number lying between the two groups, and hence say whether the structure is assortative or disassortative. ((c)) Name the kind of real network this pattern is typical of, choosing between a set of research fields that cite within their own area, and a food web in which predators feed on prey but not on each other.

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