h\7SrSSKrSSKJr S/rSrSr"SS5r\"S 5\R"SS S 9S S j55r g)zBGenerates graphs resembling the Internet Autonomous System networkN)py_random_staterandom_internet_as_graphcSSKJn X:deSU-U- nXC"U5- S- n[UR5U"U5U- -U-5nUR5U:aSnXg-$SnXg-$)aTPick a random integer with uniform probability. Returns a random integer uniformly taken from a distribution with minimum value 'a' and average value 'm', X~U(a,b), E[X]=m, X in N where b = 2*m - a. Notes ----- p = (b-floor(b))/2 X = X1 + X2; X1~U(a,floor(b)), X2~B(p) E[X] = E[X1] + E[X2] = (floor(b)+a)/2 + (b-floor(b))/2 = (b+a)/2 = m r)floor)mathrroundrandom)amseedrbpX1X2s X/var/www/html/env/lib/python3.13/site-packages/networkx/generators/internet_as_graphs.pyuniform_int_from_avgr s{ 6M6 A A U1XA t{{}a1 -1 2B {{}q  7N 7NcV[U5S:Xag[UR55nUS:Xa(UR[ UR 555$UR 5U-n[ UR 55nSnXUnX6:aUS- nX`XE- nX6:aMXE$)aPick a random value, with a probability given by its weight. Returns a random choice among degs keys, each of which has a probability proportional to the corresponding dictionary value. Parameters ---------- degs: dictionary It contains the possible values (keys) and the corresponding probabilities (values) seed: random state Returns ------- v: object A key of degs or None if degs is empty rNr)lensumvalueschoicelistkeysr )degsrsvnodesiaccs rchoose_pref_attachr#$s& 4yA~ DKKMAAv{{4 ,-- A  E A Qx.C ' Q EH~ ' 8Orc`\rSrSrSrSrSrSrSrSr Sr S r S r S r S rS rSrSrg)AS_graph_generatorGz$Generates random internet AS graphs.c$X l[U[URR5S-S-55Ul[SU-5Ul[SU-5Ul[SXR- UR - UR - 5UlSSU-S- -Ul SSU-S- -Ul S S U-S - -Ul S SU-S- -Ul S SU-S- -Ul SSU-S - -UlS UlS UlSUlg)aInitializes variables. Immediate numbers are taken from [1]. Parameters ---------- n: integer Number of graph nodes seed: random state Indicator of random number generation state. See :ref:`Randomness`. Returns ------- GG: AS_graph_generator object References ---------- [1] A. Elmokashfi, A. Kvalbein and C. Dovrolis, "On the Scalability of BGP: The Role of Topology Growth," in IEEE Journal on Selected Areas in Communications, vol. 28, no. 8, pp. 1250-1261, October 2010. rg333333?皙?rg@i'g?ri皙?g?g?N)rminr r n_tn_mn_cpmaxn_cd_md_cpd_cp_m_mp_cp_mp_cp_cpt_mt_cpt_c)selfnrs r__init__AS_graph_generator.__init__Js, q% 0 0 2Q 6 :;<?$(O q!hh,1DII=>a5((qE)) A''!a%5( QUeO+ q1u..  rc[R"5Ul[UR5HnURR USS9 UR H!nUR URU5 M# URR5HnX:wdM URXS5 M [5URU'[5URU'M UR$)zuGenerates the core mesh network of tier one nodes of a AS graph. Returns ------- G: Networkx Graph Core network T)typepeer) nxGraphGranger-add_noderegionsaddr add_edgeset customers providers)r;r!rjs rt_graphAS_graph_generator.t_graphrstxxA FFOOACO (\\ Q##A&"VV\\^6MM!/$!$DNN1  #DNN1 !vv rc`US:Xa [U5nOSnURRXX4S9 g)Ntransitnone)rAcustomer)strrErJ)r;r!rOkindrUs rrJAS_graph_generator.add_edges, 9 1vHH 4;rc~0nUH!nURRUSX#'M# [X R5$)zPick a node with a probability weighted by its peer degree. Pick a node from node_list with preferential attachment computed only on their peer degree peers)rEr r#r)r; node_listdr<s rchoose_peer_pref_attach*AS_graph_generator.choose_peer_pref_attachs: A66<<?7+AD!!YY//rct[URRU55n[X R5$)zPick a node with a probability weighted by its degree. Pick a node from node_list with preferential attachment computed on their degree )dictrEdegreer#r)r;r[rs rchoose_node_pref_attach*AS_graph_generator.choose_node_pref_attachs*DFFMM),-!$ 22rc URURU5 URURU5 URUH?nURURU5 URURU5 MA g)z=Keep the dictionaries 'customers' and 'providers' consistent.N)rLrIrM)r;r!rOzs r add_customerAS_graph_generator.add_customerss qa  qa "A NN1  ! !! $ NN1  ! !! $#rcSnURR5U:aSn[5nURR XSS9 [5UR U'[5UR U'URURU5 URR[UR5U5H?nURURU5nURURU5 MA [SX@R5n URURS5n URURS5n X;aU RU5 Sn X:a[!U 5S:d[!U 5S:a[!U 5S:Xd-[!U 5S:aAURR5U:a#UR#U 5n U RU 5 O"UR#U 5n U RU 5 UR%XS5 UR'X5 U S- n X:a"[!U 5S:aM[!U 5S:aMU$)a6Add a node and its customer transit edges to the graph. Parameters ---------- i: object Identifier of the new node kind: string Type of the new node. Options are: 'M' for middle node, 'CP' for content provider and 'C' for customer. reg2prob: float Probability the new node can be in two different regions. avg_deg: float Average number of transit nodes of which node i is customer. t_edge_prob: float Probability node i establish a customer transit edge with a tier one (T) node Returns ------- i: object Identifier of the new node rrr)rArZr@MrS)rr rKrErGrLrMr rIsamplerrHunionr intersectionremoverrbrJrf)r;r!rWreg2probavg_deg t_edge_probregs node_optionsrNedge_num t_options m_optionsr\rOs rrGAS_graph_generator.add_nodes0 99    (Du  A.EqEq 4Q!!$t||"4d;A'--dll1o>L LLO   "<(7II> --djjo>  --djjo> >   Q  lI 2c)nq6H9~"I"tyy'7'7'9K'G00;  #00;  # MM! *   a # FAlI 2c)nq6Hrc,URSRURU5nURURU5nX;aUR U5 UR R U5HnXC;dM UR U5 M [U5S:alURU5nURXS5 UR RUS==S- ss'UR RUS==S- ss'gg)a/Add a peering link between two middle tier (M) nodes. Target node j is drawn considering a preferential attachment based on other M node peering degree. Parameters ---------- m: object Node identifier to_kind: string type for target node j (must be always M) Returns ------- success: boolean rirrBrZrTF) r differencerLrMrmrE neighborsrr]rJ)r;r to_kindrrrOs radd_m_peering_link%AS_graph_generator.add_m_peering_links&zz#11$..2CD #..t~~a/@A     "!!!$A ##A&% | q ,,\:A MM! ' FFLLOG $ ) $ FFLLOG $ ) $rc[5nURH5nXRU;dMURURU5nM7 URUR U5nX;aUR U5 UR URU5nURRU5HnXS;dM UR U5 M [U5S:aURR[U5S5SnURXS5 URRUS==S- ss'URRUS==S- ss'gg)a5Add a peering link to a content provider (CP) node. Target node j can be CP or M and it is drawn uniformly among the nodes belonging to the same region as cp. Parameters ---------- cp: object Node identifier to_kind: string type for target node j (must be M or CP) Returns ------- success: boolean rrrBrZTF)rKrHrkr rlrmrxrMrEryrrrjrrJ)r;cprzrrrNrOs radd_cp_peering_link&AS_graph_generator.add_cp_peering_links6$u A\\!_$+11$,,q/B  zz'*77 E       #$..t~~b/AB !!"%A ##A&& | q    l!3Q7:A MM" ( FFLL W % * % FFLLOG $ ) $rc|0Ul[U5H&n[5URS[U5-'M( g)zYInitializes AS network regions. Parameters ---------- rn: integer Number of regions REGN)rHrFrKrV)r;rnr!s r graph_regions AS_graph_generator.graph_regions?s1 rA+.5DLLQ (rc4SnUS:XaURnURnUS:Xa+URnUS:Xa URnO URnUR UH4n[ SWUR5n[U5H nU"XR5 M M6 g)z8Utility function to add peering links among node groups.NriCPr) r{r5rr6r7r rrrF)r; from_kindrzpeer_link_methodr r!num_s radd_peering_links$AS_graph_generator.add_peering_linksLs  #66  A  #77 #~KKLLI&A&q!TYY7C3Z , 'rc 0URS5 0Ul0Ul[5[5[5[5S.UlUR 5 [UR R 55URS'[URS5n[UR5HMnURSRURUSSURUR55 US- nMO [UR5HMnURSRURUSSURUR 55 US- nMO [UR"5HMnURS RURUS S UR$UR&55 US- nMO UR)SS5 UR)SS5 UR)SS5 UR $) aGenerates a random AS network graph as described in [1]. Returns ------- G: Graph object Notes ----- The process steps are the following: first we create the core network of tier one nodes, then we add the middle tier (M), the content provider (CP) and the customer (C) nodes along with their transit edges (link i,j means i is customer of j). Finally we add peering links between M nodes, between M and CP nodes and between CP node couples. For a detailed description of the algorithm, please refer to [1]. References ---------- [1] A. Elmokashfi, A. Kvalbein and C. Dovrolis, "On the Scalability of BGP: The Role of Topology Growth," in IEEE Journal on Selected Areas in Communications, vol. 28, no. 8, pp. 1250-1261, October 2010. r*)r@rirCr@rir+rrr)rr)rrLrMrKr rPrErrFr.rIrGr2r8r/r3r9r1r4r:r)r;r!rs rgenerateAS_graph_generator.generate^s. 15suCEF  dfflln- 3  3 txxA JJsO   ac488TXX N O FA!tyy!A JJt  q$dii!S T FA"txxA JJsO   aa488 L M FA! sC( tS) tT*vv r)rErLr4r3r2r1r/r.r-r r7r6r5rMrHrr:r9r8N)__name__ __module__ __qualname____firstlineno____doc__r=rPrJr]rbrfrGr{rrrr__static_attributes__rrr%r%GsE.&P*< 03%9v&P-^ 1-$.rr%rT)graphs returns_graphc<[X5nUR5nU$)aGenerates a random undirected graph resembling the Internet AS network Parameters ---------- n: integer in [1000, 10000] Number of graph nodes seed : integer, random_state, or None (default) Indicator of random number generation state. See :ref:`Randomness`. Returns ------- G: Networkx Graph object A randomly generated undirected graph Notes ----- This algorithm returns an undirected graph resembling the Internet Autonomous System (AS) network, it uses the approach by Elmokashfi et al. [1]_ and it grants the properties described in the related paper [1]_. Each node models an autonomous system, with an attribute 'type' specifying its kind; tier-1 (T), mid-level (M), customer (C) or content-provider (CP). Each edge models an ADV communication link (hence, bidirectional) with attributes: - type: transit|peer, the kind of commercial agreement between nodes; - customer: , the identifier of the node acting as customer ('none' if type is peer). References ---------- .. [1] A. Elmokashfi, A. Kvalbein and C. Dovrolis, "On the Scalability of BGP: The Role of Topology Growth," in IEEE Journal on Selected Areas in Communications, vol. 28, no. 8, pp. 1250-1261, October 2010. )r%r)r<rGGrEs rrrsP A $B A Hr)N) rnetworkxrCnetworkx.utilsr__all__rr#r% _dispatchablerrrrrs\H* % &6 FEEP T2( 3( r