Network Structure & Centrality

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Abstractions about the structure and connectivity of networks, including measures of node importance (betweenness centrality, Katz centrality), models of network growth and community formation (fitness model, Louvain method, triadic closure), and global structural properties (small-world network, modularity, weighted network).

12 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• Betweenness centrality — A network centrality measure equal to the fraction or count of shortest paths between other vertices that pass through a given vertex or edge.
• Biased random walk on a graph — A graph random walk whose transition probabilities favor neighbors according to weights, attributes or a state-dependent bias rather than choosing uniformly.
• Community structure — A network organization in which nodes form groups with denser or more probable internal ties than ties between groups.
• Fitness model (network theory) — A growing-network model in which each node’s intrinsic fitness multiplies or otherwise modulates preferential attachment to determine link acquisition.
• Katz centrality — A network score summing all walks ending at a node with geometrically decreasing weight plus an exogenous baseline.
• Local World Evolving Network Models — Evolving-network models in which a new node samples a limited local candidate set and attaches preferentially or otherwise within that partial view.
• Louvain method — A greedy multilevel network algorithm that alternates local modularity-improving node moves with aggregation of discovered communities.
• Modularity (networks) — A network-quality measure comparing the observed density of within-community edges with the density expected under a declared null model.
• Nearest neighbor search — The optimization problem of finding dataset items minimizing a specified distance or dissimilarity to a query.
• Small-world network — A network combining high local clustering with short typical path lengths, often comparable to a regular lattice locally and a random graph globally.
• Triadic closure — The tendency for two nodes sharing a neighbor to become directly connected.
• Weighted network — A network whose edges carry numerical weights representing strength, capacity, cost, frequency, distance or another declared relation magnitude.