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This graph becomes disconnected when the right-most node in the gray area on the left is removed This graph becomes disconnected when the dashed edge is removed.. In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more ...
In certain situations, the need for belonging may overcome the physiological and security needs, depending on the strength of the peer pressure. In contrast, for some individuals, the need for self-esteem is more important than the need for belonging; and for others, the need for creative fulfillment may supersede even the most basic needs. [25]
An example graph, with 6 vertices, diameter 3, connectivity 1, and algebraic connectivity 0.722 The algebraic connectivity (also known as Fiedler value or Fiedler eigenvalue after Miroslav Fiedler) of a graph G is the second-smallest eigenvalue (counting multiple eigenvalues separately) of the Laplacian matrix of G. [1]
The algorithm for weak components generates the strongly connected components in this order, and maintains a partition of the components that have been generated so far into the weak components of their induced subgraph. After all components are generated, this partition will describe the weak components of the whole graph. [2] [3]
A graph that is locally H is claw-free if and only if the independence number of H is at most two; for instance, the graph of the regular icosahedron is claw-free because it is locally C 5 and C 5 has independence number two. The locally linear graphs are the graphs in which every neighbourhood is an induced matching. [5]
By the handshaking lemma, these two positions belong to the same connected component of the graph, and a path from one to the other necessarily passes through the desired meeting point. [ 14 ] The reconstruction conjecture concerns the problem of uniquely determining the structure of a graph from the multiset of subgraphs formed by removing a ...
The need for affiliation (N-Affil) is a term which describes a person's need to feel a sense of involvement and "belonging" within a social group.The term was popularized by David McClelland, whose thinking was strongly influenced by the pioneering work of Henry Murray, who first identified underlying psychological human needs and motivational processes in 1938.
A planar graph and its minimum spanning tree. Each edge is labeled with its weight, which here is roughly proportional to its length. A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. [1]
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