In theory of graphs, intensity of interlinking between nodes through edges of a network; more generally, degree of internal connection of a network. As opposed to mere proximity relations, called relations in continuity, connectivity relations are those using the support of a network to link two places that may be far apart from each other.
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Graph
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Connectivity
6 October 2004, by D. P. 
Network
6 October 2004, by L. C.A network is a set of elements that may be material, the infrastructure, and immaterial, electromagnetic (waves) or informational, which ensure the establishment of relations between different places of a territory and between the entities that are occupying them.
It comprises not only linear, permanent or temporary, elements which express the existence of relationships and ensure that they are possible, but also nodal elements needed in order to organise flows and to make the system in (...) 
Hierarchy
6 October 2004, by D. P.The notion of hierarchy is used with two distinct meanings. It is a social, political or administrative organisation in levels where each element belonging to a level is strictly subordinated to an element of upper level. The higher it is gone in the order of power or domination, the fewer elements are comprised in each level: hierarchy implies a pyramidal organisation. The benefit of such form of organisation is to allow making information circulate or imposing decisions while reducing (...)

Graph
6 October 2004, by L. C.Intuitively, a graph is a diagram composed of a set of points and a set of arrows, each linking two of those points. The points are called the nodes of the graph and the arrows are called the arcs of the graph.
In a more formalised way, Claude Berge defines a graph G as the datum of the (X, U) pair, where X and U respectively designate, a set of points x1, x2,..., xn called set of nodes, and a family u1, u2,..., umof elements of the Cartesian product :
X × X = (x, y) / x ∈ X, y (...)