'Advanced Network Analysis / Pajek: Large ... - Vladimir Batagelj

More documents

Recommendations

Info

V. Batagelj: Analysis and visulization of large networks with Pajek 101 ✬ ✫ Multiplication of networks To a simple two-mode network N = (I, J, E, w); where I and J are sets of vertices, E is a set of edges linking I and J, and w : E → R (or some other semiring) is a weight; we can assign a network matrix W = [wi,j] with elements: wi,j = w(i, j) for (i, j) ∈ E and wi,j = 0 otherwise. Given a pair of compatible networks NA = (I, K, EA, wA) and NB = (K, J, EB, wB) with corresponding matrices AI×K and BK×J we call a product of networks NA and NB a network NC = (I, J, EC, wC), where EC = {(i, j) : i ∈ I, j ∈ J, ci,j �= 0} and wC(i, j) = ci,j for (i, j) ∈ EC. The product matrix C = [ci,j]I×J = A ∗ B is defined in the standard way ci,j = � k∈K ai,k · bk,j In the case when I = K = J we are dealing with ordinary one-mode networks (with square matrices). Methodenforum der Fakultät für Sozialwissenschaften, Universität Wien, 21-22. 6. 2007 ▲ ❙ ▲ ▲ ● ❙ ▲ ▲ ☛ ✖ ▲ ✩ ✪
V. Batagelj: Analysis and visulization of large networks with Pajek 102 ✬ Fast sparse matrix multiplication The standard matrix multiplication has the complexity O(|I| · |K| · |J|) – it is (usually) too slow to be used for large networks. For sparse large networks we can multiply faster considering only nonzero elements: for k in K do for i in NA(k) do for j in NB(k) do if ∃ci,j then ci,j := ci,j + ai,k ∗ bk,j else new ci,j := ai,k ∗ bk,j NA(k): neighbors of vertex k in network A NB(k): neighbors of vertex k in network B In general the multiplication of large sparse networks is a ’dangerous’ operation since the result can ’explode’ – it is not sparse. ✫ Methodenforum der Fakultät für Sozialwissenschaften, Universität Wien, 21-22. 6. 2007 ▲ ❙ ▲ ▲ ▲ ● ❙ ▲ ▲ ☛ ✖ ✩ ✪
Page 1 and 2:
✬ Vienna, St. Stephen’s Cathedr
Page 3 and 4:
V. Batagelj: Analysis and visulizat
Page 5 and 6:
Page 7 and 8:
Page 9 and 10:
Page 11 and 12:
Page 13 and 14:
Page 15 and 16:
Page 17 and 18:
Page 19 and 20:
Page 21 and 22:
Page 23 and 24:
Page 25 and 26:
Page 27 and 28:
Page 29 and 30:
Page 31 and 32:
Page 33 and 34:
Page 35 and 36:
Page 37 and 38:
Page 39 and 40:
Page 41 and 42:
Page 43 and 44:
Page 45 and 46:
Page 47 and 48:
Page 49 and 50:
Page 51 and 52:
Page 53 and 54: V. Batagelj: Analysis and visulizat
Page 103: V. Batagelj: Analysis and visulizat
show all

'Advanced Network Analysis / Pajek: Large ... - Vladimir Batagelj

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?