A graph is a set of vertices and a set of lines between pairs of vertices.
A vertex (singular of vertices) is the smallest unit in a network.
A line is a relation between two vertices in a network.. A line is defined by its two endpoints, which are the two vertices that are incident with the line.
A loop is a special kind of line, namely a line which connects a vertex to itself.
An arc is an ordered pair of vertices in which the first vertex is the sender (the tail of the arc) and the second the receiver of the relation (the head of the arc).
An edge , which has no direction, is represented by an unordered pair. It does not matter which vertex is first or second in the pair.
A directed graph or digraph contains one or more arcs.
An undirected graph does not contain arcs: all of its lines are edges.
A simple undirected graph contains neither multiple edges nor loops.
A simple directed graph does not contain multiple arcs.
A network consists of a graph and additional information on the vertices or the lines of the graph.
A partition of a networks is a classification or clustering of the vertices in the networks such that each vertex is assigned to exactly one class or cluster.
Open the trade network and energize the positions of the core countries only. Hint: create a new partition where core countries belong to class zero and others to class one or higher and energize it with Fix selected networks command.
A semiwalk from vertex u to vertex v is a sequence of lines such that the end vertex of one line is the starting vertex of the next line and the sequence starts at vertex u and ends at vertex v.
A walk is a semiwalk with the additional condition that none of its lines are an arc of which the end vertex is the arc’s tail.
A cycle or semicycle is clusterable if it does not contain exactly one negative arc.
A signed graph is clusterable if it can be partitioned into clusters such that all positive ties are contained within clusters and all negative ties are situated between clusters.
Degree centralization of the network is the variation in the degrees of verticies divided by the maximum degree variation which is possible in a network of the same size.
The closeness centrality of a vertex is the number of other vertices divided by the sum of all distances between the vertex and all others.
Closeness centralization is the variation in the closeness centrality of vertices divided by the maximum variation in closeness centrality scores possible in a network of the same size.
What will happen to the network if Juan (HM-1) disappears? Remove the vertex, compare closeness centrality and centralization and interpret the results.
The betweenness centrality of a vertex is the proportion of all geodesics between pairs of other vertices that include this vertex.
Betweenness centralization is the vairation in the betweenness centrality of vertices divided by the maximum vairiation in betweenness centrality scores possible in an network of the same size.
The dyadic constraint on a vertex u exercised by a tie between vertices u and v is the extent to which u has more and stronger ties with neighbors who are strongly connected to vertex v .
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