Network Evolution & Community Structure

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Abstractions about network formation, decentralization, centrality, communities, modularity, closure, and flow. They include random-walk and fitness models, small-world and evolving networks, block models, community-detection methods, weighted graphs, and structural transformations.

19 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.

• Bak–Sneppen model — An extremal coevolution model that repeatedly replaces the least-fit species and its neighbors, self-organizing toward a critical fitness threshold and avalanche dynamics.
• Berkeley algorithm — A distributed clock-synchronization algorithm in which an elected leader estimates participant clocks, rejects outliers and sends relative adjustments toward their average.
• 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.
• Blockmodeling — A social-network analysis framework that partitions actors into position classes whose tie patterns form an interpretable reduced block structure.
• Centrality — A family of graph measures that ranks vertices or edges by a declared notion of structural importance.
• Community structure — A network organization in which nodes form groups with denser or more probable internal ties than ties between groups.
• Decentralised system — A system in which components use local information and interaction to coordinate behavior without one controlling center.
• 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.
• Power graph analysis — Lossless graph compression and visualization by grouping repeated clique, biclique, and star connection patterns.
• Shortcut model — A random-network model that interpolates between regular lattices of neighboring integer dimensions by adding structured long-range shortcut layers.
• Signal-flow graph — A directed weighted graph whose nodes denote system variables and whose branches denote functional dependence or gain from one variable to another.
• 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.
• Star-mesh transform — A circuit-network reduction that eliminates a central node by replacing its incident star branches with pairwise mesh impedances preserving terminal behavior.
• 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.