Network theory

In mathematics, computer science and network science, network theory is a part of graph theory. It defines networks as graphs where the nodes or edges possess attributes. Network theory analyses these networks over the symmetric relations or asymmetric relations between their (discrete) components.

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Network science
Theory
Graph Complex network Contagion Small-world Scale-free Community structure Percolation Evolution Controllability Graph drawing Social capital Link analysis Optimization Reciprocity Closure Homophily Transitivity Preferential attachment Balance theory Network effect Social influence
Network types
Informational (computing) Telecommunication Transport Social Scientific collaboration Biological Artificial neural Interdependent Semantic Spatial Dependency Flow on-Chip
Graphs
Features Clique Component Cut Cycle Data structure Edge Loop Neighborhood Path Vertex Adjacency list / matrix Incidence list / matrix Types Bipartite Complete Directed Hyper Labeled Multi Random Weighted
Metrics Algorithms
Centrality Degree Motif Clustering Degree distribution Assortativity Distance Modularity Efficiency
Models
Topology Random graph Erdős–Rényi Barabási–Albert Bianconi–Barabási Fitness model Watts–Strogatz Exponential random (ERGM) Random geometric (RGG) Hyperbolic (HGN) Hierarchical Stochastic block Blockmodeling Maximum entropy Soft configuration LFR Benchmark Dynamics Boolean network agent based Epidemic/SIR
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Topics Software Network scientists Category:Network theory Category:Graph theory
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Network theory has applications in many disciplines, including statistical physics, particle physics, computer science, electrical engineering,[1][2] biology,[3] archaeology,[4] linguistics,[5][6][7] economics, finance, operations research, climatology, ecology, public health,[8][9][10] sociology,[11] psychology,[12] and neuroscience.[13][14][15] Applications of network theory include logistical networks, the World Wide Web, Internet, gene regulatory networks, metabolic networks, social networks, epistemological networks, etc.; see List of network theory topics for more examples.

Euler's solution of the Seven Bridges of Königsberg problem is considered to be the first true proof in the theory of networks.