wg\7dZddlZddlmZdgZdZdZGddZed ejdd d d Z y)zBGenerates graphs resembling the Internet Autonomous System networkN)py_random_staterandom_internet_as_graphcddlm}||k\sJd|z|z }|||z dz }t|j|||z z|z}|j|krd}||zSd}||zS)axPick 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 k/home/mcse/projects/flask/flask-venv/lib/python3.12/site-packages/networkx/generators/internet_as_graphs.pyuniform_int_from_avgr s 6M6 A A U1XA t{{}a1 -1 2B {{}q  7N 7NcXt|dk(ryt|j}|dk(r(|jt |j S|j |z}t |j }d}|||}||kDr|dz }||||z }||kDr||S)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#$s& 4yA~ DKKMAAv{{4 ,-- A  E A uQx.C c' Q tE!H~ c' 8OrcXeZdZdZdZdZdZdZdZdZ dZ d Z d Z d Z d Zd Zy)AS_graph_generatorz$Generates random internet AS graphs.c(||_t|t|jjdzdz|_td|z|_td|z|_td||jz |j z |j z |_dd|zdz z|_ dd|zdz z|_ d d |zd z z|_ d d|zdz z|_ d d|zdz z|_ dd|zd z z|_d |_d |_d|_y)avInitializes 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__zAS_graph_generator.__init__Js , q% 0 0 2Q 6 :;<?$(O q!dhh,1DII=>a5((qE)) A''!a%5( QUeO+ q1u..  rctj|_t|jD]}|jj |d|j D] }|j |j|"|jjD]}||k7s |j||dt|j|<t|j|<|jS)zGenerates the core mesh network of tier one nodes of a AS graph. Returns ------- G: Networkx Graph Core network T)typepeer) nxGraphGranger,add_noderegionsaddr add_edgeset customers providers)r:r!rjs rt_graphzAS_graph_generator.t_graphrstxx &A FFOOACO (\\ ' Q##A& 'VV\\^ 06MM!Q/ 0!$DNN1  #DNN1  &vv rch|dk(r t|}nd}|jj||||y)Ntransitnone)r?customer)strrCrH)r:r!rMkindrRs rrHzAS_graph_generator.add_edges0 9 1vHH 14(;rc~i}|D]!}|jj|d||<#t||jS)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)rCr r#r)r: node_listdr;s rchoose_peer_pref_attachz*AS_graph_generator.choose_peer_pref_attachsC  ,A66<<?7+AaD ,!!TYY//rcvt|jj|}t||jS)zPick a node with a probability weighted by its degree. Pick a node from node_list with preferential attachment computed on their degree )dictrCdegreer#r)r:rWrs rchoose_node_pref_attachz*AS_graph_generator.choose_node_pref_attachs,DFFMM),-!$ 22rc|j|j||j|j||j|D]>}|j|j||j|j|@y)z=Keep the dictionaries 'customers' and 'providers' consistent.N)rJrGrK)r:r!rMzs r add_customerzAS_graph_generator.add_customersx qa  qa " %A NN1  ! !! $ NN1  ! !! $ %rcd}|jj|krd}t}|jj ||dt|j |<t|j |<|j|j||jjt|j|D]>}|j|j|}|j|j|@td||j} |j|jd} |j|jd} || vr| j|d} | | krt!| dkDst!| dkDrt!| dk(s+t!| dkDr@|jj|kr#|j#| } | j| n"|j#| } | j| |j%|| d|j'|| | dz } | | krt!| dkDrt!| dkDr|S)aAdd 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)r?rVr>MrP)rr rIrCrErJrKr rGsamplerrFunionr intersectionremoverr]rHr`)r:r!rTreg2probavg_deg t_edge_probregs node_optionsrLedge_num t_options m_optionsrXrMs rrEzAS_graph_generator.add_nodes0 99    (Du  A.EqEq 4Q!!$t||"4d; #A'--dll1o>L LLO   " #(7DII> --djjo>  --djjo> >   Q  (lI 2c)nq6H9~"I"tyy'7'7'9K'G00;  #00;  # MM!Q *   a # FA(lI 2c)nq6Hrc"|jdj|j|}|j|j|}||vr|j ||j j |D]}||vs|j |t|dkDrm|j|}|j||d|j j|dxxdz cc<|j j|dxxdz cc<yy)aAdd a peering link between two middle tier (M) nodes. Target node j is drawn considering a preferential attachment based on other M node peering degree. Parameters ---------- m: object Node identifier to_kind: string type for target node j (must be always M) Returns ------- success: boolean rbrr@rVrTF) r differencerJrKrfrC neighborsrrYrH)r:r to_kindrkrMs radd_m_peering_linkz%AS_graph_generator.add_m_peering_links&zz#11$..2CD #..t~~a/@A     "!!!$ 'AL ##A& ' | q ,,\:A MM!Q ' FFLLOG $ ) $ FFLLOG $ ) $rct}|jD]2}||j|vs|j|j|}4|j|j |}||vr|j ||j |j|}|jj|D]}||vs|j |t|dkDr|jjt|dd}|j||d|jj|dxxdz cc<|jj|dxxdz cc<yy)aAdd a peering link to a content provider (CP) node. Target node j can be CP or M and it is drawn uniformly among the nodes belonging to the same region as cp. Parameters ---------- cp: object Node identifier to_kind: string type for target node j (must be M or CP) Returns ------- success: boolean rrr@rVTF)rIrFrdr rerfrprKrCrqrrrcrrH)r:cprrrkrLrMs radd_cp_peering_linkz&AS_graph_generator.add_cp_peering_linksJ$u  CAT\\!_$+11$,,q/B  C zz'*77 E       #$..t~~b/AB !!"% 'AL ##A& ' | q    l!3Q7:A MM"a ( FFLL W % * % FFLLOG $ ) $rcxi|_t|D]%}t|jdt|z<'y)zInitializes AS network regions. Parameters ---------- rn: integer Number of regions REGN)rFrDrIrS)r:rnr!s r graph_regionsz AS_graph_generator.graph_regions?s6 r 1A+.5DLLQ ( 1rc(d}|dk(r|j}|j}|dk(r*|j}|dk(r |j}n |j}|j |D]2}t d|j}t|D] }||| 4y)z8Utility function to add peering links among node groups.NrbCPr) rsr4rvr5r6r rrrD)r: from_kindrrpeer_link_methodr r!num_s radd_peering_linksz$AS_graph_generator.add_peering_linksLs  #66  A  #77 #~KKLLI& -A&q!TYY7C3Z - G, - -rc $|jdi|_i|_ttttd|_|j t|j j |jd<t|jd}t|jD]L}|jdj|j|dd|j|j|dz }Nt|jD]L}|jdj|j|dd|j|j |dz }Nt|j"D]L}|jd j|j|d d |j$|j&|dz }N|j)dd|j)dd|j)dd|j S) aiGenerates 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>rbr|Cr>rbr*rr|r(rr)rzrJrKrIr rNrCrrDr-rGrEr1r7r.r2r8r0r3r9r)r:r!rs rgeneratezAS_graph_generator.generate^s. 15suCEF  dfflln- 3  3 txx A JJsO   ac488TXX N O FA tyy! A JJt  q$dii!S T FA txx A JJsO   aa488 L M FA  sC( tS) tT*vv rN)__name__ __module__ __qualname____doc__r<rNrHrYr]r`rErsrvrzrrrrr%r%GsE.&P*< 03%9v&P-^ 1-$.rr%rT)graphs returns_graphc>t||}|j}|S)aJGenerates 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;rGGrCs rrrs!P At $B A Hr)N) rnetworkxrAnetworkx.utilsr__all__rr#r% _dispatchablerrrrrs^H* % &6 FEEP T2( 3( r