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A drawing of a graph with 6 vertices and 7 edges.. In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
The main difference between modular decomposition and power graph analysis is the emphasis of power graph analysis in decomposing graphs not only using modules of nodes but also modules of edges (cliques, bicliques). Indeed, power graph analysis can be seen as a loss-less simultaneous clustering of both nodes and edges.
In statistical physics and mathematics, percolation theory describes the behavior of a network when nodes or links are added. This is a geometric type of phase transition, since at a critical fraction of addition the network of small, disconnected clusters merge into significantly larger connected, so-called spanning clusters.
The analysis of electric power systems could be conducted using network theory from two main points of view: An abstract perspective (i.e., as a graph consists from nodes and edges), regardless of the electric power aspects (e.g., transmission line impedances).
A chordal graph is a graph whose vertices can be ordered into a perfect elimination ordering, an ordering such that the neighbors of each vertex v that come later than v in the ordering form a clique. A cograph is a graph all of whose induced subgraphs have the property that any maximal clique intersects any maximal independent set in a single ...
Graph theory has close links to group theory. This truncated tetrahedron graph is related to the alternating group A 4. Graph theory, the study of graphs and networks, is often considered part of combinatorics, but has grown large enough and distinct enough, with its own kind of problems, to be regarded as a subject in its own right. [14]
Discrete geometric analysis created and developed by Toshikazu Sunada in the 2000s deals with spectral graph theory in terms of discrete Laplacians associated with weighted graphs, [18] and finds application in various fields, including shape analysis. In most recent years, the spectral graph theory has expanded to vertex-varying graphs often ...
The distributions of a wide variety of physical, biological, and human-made phenomena approximately follow a power law over a wide range of magnitudes: these include the sizes of craters on the moon and of solar flares, [2] cloud sizes, [3] the foraging pattern of various species, [4] the sizes of activity patterns of neuronal populations, [5] the frequencies of words in most languages ...