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NetworkX is suitable for operation on large real-world graphs: e.g., graphs in excess of 10 million nodes and 100 million edges. [ clarification needed ] [ 19 ] Due to its dependence on a pure-Python "dictionary of dictionary" data structure, NetworkX is a reasonably efficient, very scalable , highly portable framework for network and social ...
In particular, this shows that any maximal matching is a 2-approximation of a maximum matching and also a 2-approximation of a minimum maximal matching. This inequality is tight: for example, if G is a path with 3 edges and 4 vertices, the size of a minimum maximal matching is 1 and the size of a maximum matching is 2.
More precisely, when t edges have been added, for values of t close to but larger than /, the size of the giant component is approximately . [1] However, according to the coupon collector's problem , Θ ( n log n ) {\displaystyle \Theta (n\log n)} edges are needed in order to have high probability that the whole random graph is connected.
The betweenness centrality of a node is given by the expression: = ()where is the total number of shortest paths from node to node and () is the number of those paths that pass through (not where is an end point).
In an unweighted undirected graph, the size or weight of a cut is the number of edges crossing the cut. In a weighted graph, the value or weight is defined by the sum of the weights of the edges crossing the cut. A bond is a cut-set that does not have any other cut-set as a proper subset.
Example of modularity measurement and colouring on a scale-free network.. Modularity is a measure of the structure of networks or graphs which measures the strength of division of a network into modules (also called groups, clusters or communities).
NetworkX, an open source Python library for studying complex graphs. Tulip (software) is a free software in the domain of information visualisation capable of manipulating huge graphs (with more than 1.000.000 elements). yEd, a free Java-based graph editor, supports import from and export to GML.
Force-directed graph drawing algorithms assign forces among the set of edges and the set of nodes of a graph drawing.Typically, spring-like attractive forces based on Hooke's law are used to attract pairs of endpoints of the graph's edges towards each other, while simultaneously repulsive forces like those of electrically charged particles based on Coulomb's law are used to separate all pairs ...