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# Effectiveness

#### Definition

In a connected network, you can calculate degree for each node. Let's call Dj the degree for "j" node. For two linked nodes i and j, the effect of i on j is 1/Dj, the reciprocal value of the degree of j. This means that the more neighbors you have, the less one of them matters on influencing you. For a two-step long effect from i to j to k, the effect of i on k is the multiplication of the ij and jk effects, so it equals 1/Dj * 1/Dk.
For two parallel effects of the same length, the effects are additive: if i influences k through j (i-j-k) and m (i-m-k), then the two-steps effect pf i on k equals 1/Dj*1/Dk + 1/Dm*1/Dk.
Note that ij and ji effects are not necessarily equal.
For a given step number, you can calculate all of these pairwise effects. Summing these values, we can have a number describing the importance of the node i in the network: the bigger the number, the more effect on other nodes.

In Biological Terms
In biological systems, more than three-step effects are very small compared with other less-steps effects: in our calculation we don't consider them. Effectiveness can describe the unicality of node i in the network, meaning the effect this node has on others and its non-redundant role among the others.

#### References

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