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Real life examples of negative weight edges in graphs
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Problem
I am unable to relate to any real life examples of negative weight edges in graphs. Distances between cities cannot be negative. Time taken to travel from one point to another cannot be negative. Data transfer rates cannot be negative. I am just blanking out while thinking of negative weight edges in graphs.
Can we have a list of say 6 or 7 real-life examples where negative weights make intuitive sense?
Can we have a list of say 6 or 7 real-life examples where negative weights make intuitive sense?
Solution
Distance between cities can't be negative, but if you are programming for an electric car, then a downhill road segment will regen, thus the energy used is negative. It is very important to take that into account when predicting range.
In a neural network, we can use negative weights to indicate that one neuron firing is inversely correlated with another neuron.
In a clustering network we can use negative edges to indicate that two points should certainly not belong together. This is also relevant in community detection.
In sports, you can use a directed edge from $a$ to $b$ to mean the likelihood that $a$ will win against $b$ when $a$ is home team. In general, when we have non-symmetric relationships, $a\to b$ is different from $b \to a$ and we can't necessarily encode negative numbers with reverse arcs. This is also relevant in finance where $a \to b$ can mean that $a$ either owes money or $b$ owes money. The direction of the arrow can mean who is responsible for the transaction to take place.
Attractive and repulsive forces are used both in graph drawing, but also in particle simulation and simulation of other dynamical systems. These are often undirected positive or negative edges. In simulation of fluids, you will also have negative values denoting different forms of pressures from one area to another.
In a neural network, we can use negative weights to indicate that one neuron firing is inversely correlated with another neuron.
In a clustering network we can use negative edges to indicate that two points should certainly not belong together. This is also relevant in community detection.
In sports, you can use a directed edge from $a$ to $b$ to mean the likelihood that $a$ will win against $b$ when $a$ is home team. In general, when we have non-symmetric relationships, $a\to b$ is different from $b \to a$ and we can't necessarily encode negative numbers with reverse arcs. This is also relevant in finance where $a \to b$ can mean that $a$ either owes money or $b$ owes money. The direction of the arrow can mean who is responsible for the transaction to take place.
Attractive and repulsive forces are used both in graph drawing, but also in particle simulation and simulation of other dynamical systems. These are often undirected positive or negative edges. In simulation of fluids, you will also have negative values denoting different forms of pressures from one area to another.
Context
StackExchange Computer Science Q#146311, answer score: 35
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