Network formation & growth

Network formation and growth studies how nodes and links emerge and change over time through addition, deletion, and rewiring.

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Preferential attachment: A network-growth rule in which new nodes connect more often to nodes that already have many links. It generates hubs through cumulative advantage as a network grows.
Graph theory: The mathematical study of graphs, structures made of vertices and edges. Network growth builds on graph concepts for representing nodes and links.
Citation network: A directed network in which publications link to works they cite. New papers add nodes and preferentially cite visible, established work.
Erdős–Rényi model: A random graph model in which each possible edge is included independently with a fixed probability. Its static edge sampling contrasts with explicit node-by-node growth rules.
Triadic closure: The tendency for two nodes with a shared neighbor to form a link. It models how local neighborhoods create clustered connections during growth.
Adjacency matrix: A matrix that records which pairs of vertices in a graph are connected. Comparing adjacency matrices across time makes link changes explicit.
Social network: A network whose nodes represent social entities and whose links represent relationships or interactions. People form and revise ties through mechanisms such as shared acquaintances.
Watts–Strogatz model: A graph model that interpolates between a regular lattice and a random network through edge rewiring. It creates small-world structure by rewiring a fixed network rather than growing it.
Link rewiring: A process that removes existing network links and replaces them with links between different nodes. Rewiring changes network structure without requiring the node set to grow.
Degree distribution: The probability distribution of the number of edges incident to vertices in a graph. Growth rules often leave their clearest signature in node degrees.