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The friendship graphs F 2, F 3 and F 4. In the mathematical field of graph theory, the friendship graph (or Dutch windmill graph or n-fan) F n is a planar, undirected graph with 2n + 1 vertices and 3n edges. [1] The friendship graph F n can be constructed by joining n copies of the cycle graph C 3 with a common vertex, which becomes a universal ...
The friendship between x and y is therefore modeled by the edge {x, y}, and the number of friends an individual has corresponds to a vertex's degree. The average number of friends of a person in the social network is therefore given by the average of the degrees of the vertices in the graph.
78 of the 156 possible friends-strangers graphs with 6 nodes. The other 78 can be obtained by reversing the red and blue colours of each graph. For each graph the red/blue nodes shows a sample triplet of mutual friends/strangers. The theorem on friends and strangers is a mathematical theorem in an area of mathematics called Ramsey theory.
Dunbar's number has become of interest in anthropology, evolutionary psychology, [12] statistics, and business management.For example, developers of social software are interested in it, as they need to know the size of social networks their software needs to take into account; and in the modern military, operational psychologists seek such data to support or refute policies related to ...
Graph theory is also widely used in sociology as a way, for example, to measure actors' prestige or to explore rumor spreading, notably through the use of social network analysis software. Under the umbrella of social networks are many different types of graphs. [17] Acquaintanceship and friendship graphs describe whether people know each other.
By construction, the windmill graph Wd(3,n) is the friendship graph F n, the windmill graph Wd(2,n) is the star graph S n and the windmill graph Wd(3,2) is the ...
This Earth sign seeks friends who respect their meticulous nature and appreciate their intense connection to day-to-day affairs. Virgo enjoys friendships that offer mutual support and grounded ...
A vertex in a directed graph whose second neighborhood is at least as large as its first neighborhood is called a Seymour vertex. [5]In the second neighborhood conjecture, the condition that the graph have no two-edge cycles is necessary, for in graphs that have such cycles (for instance the complete oriented graph) all second neighborhoods may be empty or small.