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A network N = (V,L,P,W) is determined with four sets:
The set of nodes and the set of links describe its structure and form a graph G = (V,L).
A = ∅ - undirected graph
E = ∅ - directed graph
V = { a, b, c, d, e, f, g, h, i, j, k, l }
A = { (a,b), (a,d), (a,f), (b,a), (b,f), (c,b), (c,c), (c,g)1, (c,g)2, (e,c), (e,f), (e,h), (f,k), (h,d), (h,l), (j,h), (l,e), (l,g), (l,h) }
E = { (b:e), (c:d), (e:g), (f:h) }
G = ( V, (A, E) )
L = A ∪ E
The nodes are indexed starting with 1. In listing of links (arcs or edges) their end-nodes are replaced by their indices.
A line describing a node (vertex) has the following components: index, label, X, Y, Z. If the label contains a space it should be put in quotes “la bel”. Pajek's internal coordinates X, Y, Z are in the range [0,1]. If your coordinates are out of this range (for example geographical longitude and latitude) you can transform them into the Pajek's range in the drawing window using the option
Options/Transform/Fit Area
You can even skip the list of nodes - specifying only the line *vertex
n. In this case the node labels will be created automatically and the coordinates are put on the circle.
A line describing a link has the following components: 1st-node-index, 2nd-node-index, weight. If the weight is omitted the default value 1 is used.
A line starting with % is a comment line.
% Example network % by Vladimir Batagelj, April 2003 *Vertices 12 1 "a" 0.1020 0.3226 2 "b" 0.2860 0.0876 3 "c" 0.5322 0.2304 4 "d" 0.3259 0.3917 5 "e" 0.5543 0.4770 6 "f" 0.1552 0.6406 7 "g" 0.8293 0.3249 8 "h" 0.4479 0.6866 9 "i" 0.8204 0.8203 10 "j" 0.4789 0.9055 11 "k" 0.1175 0.9032 12 "l" 0.7095 0.6475 *Arcs 1 2 2 1 1 4 1 6 2 6 3 2 3 3 3 7 3 7 5 3 5 6 5 8 6 11 8 4 10 8 12 5 12 7 8 12 12 8 *Edges 2 5 3 4 5 7 6 8
GraphSet: PDF / net; TinaSet: PDF / net, PDF picture.
NA(a) = { b, d, f }
NA(b) = { a, f }
NA( c) = { b, c, g, g }
NA(e) = { c, f, h }
NA(f) = { k }
NA(h) = { d, l }
NA(j) = { h }
NA(l) = { e, g, h }
NE(e) = { b, g }
NE( c) = { d }
NE(f) = { h }
N(v) = NA(v) ∪ NE(v)
The line with node's neighbors description has a form: i0, i1, i1, …, ik with a meaning: the node i0 has neighbors i1, i1, …, ik.
*Vertices 12 1 "a" 0.1020 0.3226 2 "b" 0.2860 0.0876 3 "c" 0.5322 0.2304 4 "d" 0.3259 0.3917 5 "e" 0.5543 0.4770 6 "f" 0.1552 0.6406 7 "g" 0.8293 0.3249 8 "h" 0.4479 0.6866 9 "i" 0.8204 0.8203 10 "j" 0.4789 0.9055 11 "k" 0.1175 0.9032 12 "l" 0.7095 0.6475 *Arcslist 1 2 4 6 2 1 6 3 2 3 7 7 5 3 6 8 6 11 8 4 12 10 8 12 5 7 8 *Edgeslist 2 5 3 4 5 7 6 8
Our network can be also described using a matrix.
a b c d e f g h i j k l a 0 1 0 1 0 1 0 0 0 0 0 0 b 1 0 0 0 1 1 0 0 0 0 0 0 c 0 1 1 1 0 0 2 0 0 0 0 0 d 0 0 1 0 0 0 0 0 0 0 0 0 e 0 1 1 0 0 1 1 1 0 0 0 0 f 0 0 0 0 0 0 0 1 0 0 1 0 g 0 0 0 0 1 0 0 0 0 0 0 0 h 0 0 0 1 0 1 0 0 0 0 0 1 i 0 0 0 0 0 0 0 0 0 0 0 0 j 0 0 0 0 0 0 0 1 0 0 0 0 k 0 0 0 0 0 0 0 0 0 0 0 0 l 0 0 0 0 1 0 1 1 0 0 0 0
Graph G is simple if in the corresponding matrix all entries are 0 or 1.
In general, a matrix entry can be any real number. Each matrix line should be written in a single line with at least one space between entries as a separator.
*Vertices 12 1 "a" 0.1020 0.3226 2 "b" 0.2860 0.0876 3 "c" 0.5322 0.2304 4 "d" 0.3259 0.3917 5 "e" 0.5543 0.4770 6 "f" 0.1552 0.6406 7 "g" 0.8293 0.3249 8 "h" 0.4479 0.6866 9 "i" 0.8204 0.8203 10 "j" 0.4789 0.9055 11 "k" 0.1175 0.9032 12 "l" 0.7095 0.6475 *Matrix 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 1 1 0 0 2 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0