Infrastructure · Primitives
DegreeEntropy#a793
Entropy of how connectivity is spread over the nodes of a network: local heterogeneity
Mechanism
For a network with N nodes and degree sequence k_1..k_N, normalise each node's share of all links, p_i = k_i / sum_j k_j, and take H_d = -sum_i p_i log2 p_i, the ShannonEntropy of that share. H_d is maximal (log2 N) when every node has the same degree and falls as connectivity concentrates on a few hubs. It measures how evenly interaction opportunities are distributed, i.e. the diversity of local pathways. For a directed graph, k_i can be the total degree (in-degree plus out-degree), which discards direction. Note that p_i runs over nodes, not over degree classes, so H_d also grows with N; normalise by N or by an area to compare networks of different size.
Invariants
- Computed from the degree sequence alone, ignoring which nodes are linked to which
- Maximal when all degrees are equal, minimal when connectivity is concentrated
- Grows with node count, so raw values are not comparable across networks of different size
Failure modes
- Comparing raw H_d across networks of different size and mistaking size for structure
- Using total degree on a directed graph and losing the asymmetry between incoming and outgoing links
- Confusing this node-share form with the entropy of the degree distribution P(k)
Where this came from
- Thesis Kevin Do, PhD thesis on ant collective behaviour (NCSU, 2026), Ch. 1.3.3, Eqs. 1.6-1.7; Ch. 3.2.2, Eq. 3.26
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Identity
The name is the hash of the definition. Change a word and it becomes a different pattern.
- Sema ID
sema:DegreeEntropy#mh:SHA-256:a793cb859ab1915416e67b257770a97d4810b2ac751247aba715530df2d69297- Reference
DegreeEntropy#a793- Ring
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- Tier
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