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Questions tagged [network-theory]

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Literature on the controllability of networks under attack

I would like to request your advice on a problem arising from my research in the life sciences. Consider a modular, sparse weighted network which is partially controllable in the sense that some ...
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1answer
81 views

Number of sequences of edges that contain at least one subsequence which is a walk between vertex $i$ and $j$

Typically a walk is defined as a vertex-edge sequence, e.g. $(v_1, e_1, v_2, e_2, v_3)$, but suppose we are working in the undirected simple graph setting. Instead, let's say an edge-sequence $(e_1, ...
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When is the first blocking flow created in Dinic's algorithm a max flow?

When is the first blocking flow created in Dinic's algorithm a max flow? I understand that this is usually an iterated algorithm where one creates level graphs and augments the existing blocking flow ...
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0answers
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On the defect of a flow network

This problem in graph theory was actually motivated by some problems in Theory of Fractals. To formulate the problem I need to recall some definitions related to flow network. A flow network is a ...
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Hermann Weyl's work on combinatorial topology and Kirchhoff's current law in Spanish

Hermann Weyl was one of the pioneers in the use of early algebraic/combinatorial topological methods in the problem of electrical currents on graphs and combinatorial complexes. The ...