localassort module

Multiscale mixing patterns in networks.

Code to calculate the multiscale assortativity from the accompanying paper: Peel, L., Delvenne, J. C., & Lambiotte, R. (2018). ‘Multiscale mixing patterns in networks.’ PNAS, 115(16), 4057-4062.

localassort.calculateRWRrange(W, i, alphas, n, maxIter=1000)

Calculate the personalised TotalRank and personalised PageRank vectors.

Parameters

  • W (array_like) – transition matrix (row normalised adjacency matrix)

  • i (int) – index of the personalisation node

  • alphas (array_like) – array of (1 - restart probabilties)

  • n (int) – number of nodes in the network

  • maxIter (int, optional) – maximum number of interations (default: 1000)

Returns

  • pPageRank_all (array_like) – personalised PageRank for all input alpha values (only calculated if more than one alpha given as input, i.e., len(alphas) > 1)

  • pTotalRank (array_like) – personalised TotalRank (personalised PageRank with alpha integrated out)

  • it (int) – number of iterations

References

See 2 and 3 for further details.

2

Boldi, P. (2005). “TotalRank: Ranking without damping.” In Special interest tracks and posters of the 14th international conference on World Wide Web (pp. 898-899).

3

Boldi, P., Santini, M., & Vigna, S. (2007). “A deeper investigation of PageRank as a function of the damping factor.” In Dagstuhl Seminar Proceedings. Schloss Dagstuhl-Leibniz-Zentrum für Informatik.

localassort.createA(E, n, m, undir=True)

Create adjacency matrix and degree sequence.

localassort.localAssortF(edgelist, node_attr, pr=array([0., 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]), undir=True, missingValue=- 1)

Calculate the multiscale assortativity.

Parameters

  • edgelist (array_like) – the network represented as an edge list, i.e., a E x 2 array of node pairs

  • node_attr (array_like) – n length array of node attribute values

  • pr (array, optional) – array of one minus restart probabilities for the random walk in calculating the personalised pagerank. The largest of these values determines the accuracy of the TotalRank vector max(pr) -> 1 is more accurate (default: [0, .1, .2, .3, .4, .5, .6, .7, .8, .9])

  • undir (bool, optional) – indicate if network is undirected (default: True)

  • missingValue (int, optional) – token to indicate missing attribute values (default: -1)

Returns

  • assortM (array_like) – n x len(pr) array of local assortativities, each column corresponds to a value of the input restart probabilities, pr. Note if only number of restart probabilties is greater than one (i.e., len(pr) > 1).

  • assortT (array_like) – n length array of multiscale assortativities

  • Z (array_like) – N length array of per-node confidence scores

References

For full details see 1

1

Peel, L., Delvenne, J. C., & Lambiotte, R. (2018). “Multiscale mixing patterns in networks.’ PNAS, 115(16), 4057-4062.