Topologies {network, topology}| can have nodes {vertex, network} connected by lines {edge, network}. Two non-parallel surfaces intersect at an edge. Three non-parallel surfaces intersect at a vertex. Non-zero areas intersect at edges {path arc} {arc, boundary} {boundary, arc} and vertices and are finite in number.
connected
Networks can have one or more vertices that have only one edge. Networks {connected network} can have at least two path arcs at all vertexes.
map
Networks {map, network} can have path arcs that bound countries or regions.
path
Traveling along edges leads to vertex sequences {path}. Traveling around whole network can involve returning to vertex or never returning.
random
Keeping node number constant, nodes can have random numbers of random links to other nodes {random network} {exponential network}. Nodes have same average link number. Probability that node connects to N other nodes decreases exponentially with N. Variance can be small {Poisson distribution, network}.
hubs
Not keeping node number constant, random networks {scale-free network} can have nodes {hub} with more links than others. Probability that node connects to N other nodes is approximately proportional to (1/N)^2. Early nodes tend to have more links. Several nodes are critical. Affecting single and many random hubs is unlikely to break network. Internet, social networks, alliances, and cell biochemical reactions can be scale-free networks.
Mathematical Sciences>Topology>Polyhedron
Outline of Knowledge Database Home Page
Description of Outline of Knowledge Database
Date Modified: 2022.0224