It calculates the average length of the shortest paths between pairs of = nodes of a network. The shortest path lengths are calculated via breadth-first search.

The network to analyze must be undirected, otherwise there are no specia= l constraints. The algorithm does not take edge weight into consideration i= n calculation of average path length.

Basic analysis tool, not particular for special disciplines or problems.=

The algorithm needs only one input, the file where the edges of the netw=
ork are listed. A first read-in of the inputfile will set the values of the=
number of nodes and edges of the network. In the second read-in the edges =
are stored in an array. Then the breadth-first search process is performed =
and the histogram of the shortest path length is evaluated. From the latter=
the average path length is determined and displayed in the NWB console. Th=
e algorithm runs in a time *O(nm)*, where *n* is the number o=
f nodes, *m* the number of edges of the network. This algorithm is p=
articularly suitable for sparse networks, i.e. *if m* *n;* in that case, th=
e computational complexity is *O(n^2)*. Because of the quadratic dep=
endence on the number of nodes, the algorithm should not be applied to netw=
orks with more than *10^5* nodes.*if m *

A simple application of this algorithm could be to calculate the average= shortest path for networks created by the modeling algorithms of the NWB. = For instance, the inputfile can be created through the Barabasi-Albert mode= l.

The algorithm was implemented and documented by S. Fortunato, integrated= by S. Fortunato and W. Huang. For the description we acknowledge Wikipedia= .

Bollobas, B. (2002) Modern Graph Theory. Springer Verlag, New York.

Albert, R., and Barabasi, A.-L. (2002) Statistical mechanics of complex networks. Review of Modern Phys= ics 74:47-97.

Newman, M.E.J. (2003) Th= e structure and function of complex networks. SIAM Review 45:167-256.

Pastor-Satorras, R., Vespignani, A.(2002) Evolution and Structure of the= Internet. Cambridge University Press.

Boccaletti, S., Latora, V., Moreno, Y.,Chavez, M., Hwang, D.-U.(2006) Complex networks: Structure and dynamics. Physics= Reports 424: 175-308.

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