ó ,µ[c@sqdZddlmZddlZddlmZddgZd„Zd„Z e e d „Z d „Z d „Z d „Zd e e d„Zdd„Zd„Zdd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zed„Zd„Zd„Z d„Z!edƒdd „ƒZ"d!„Z#d"„Z$ed#ƒd$d$dd%„ƒZ%dS(&s? Threshold Graphs - Creation, manipulation and identification. iÿÿÿÿ(tsqrtN(tpy_random_statetis_threshold_graphtfind_threshold_graphcCs ttd„|jƒDƒƒƒS(s1 Returns True if G is a threshold graph. css|]\}}|VqdS(N((t.0tntd((s<lib/python2.7/site-packages/networkx/algorithms/threshold.pys s(tis_threshold_sequencetlisttdegree(tG((s<lib/python2.7/site-packages/networkx/algorithms/threshold.pyRscCsŠ|}|jƒxr|r…|ddkr=|jdƒqn|dt|ƒdkr[tS|jƒg|D]}|d^ql}qWtS(s‘ Returns True if the sequence is a threshold degree seqeunce. Uses the property that a threshold graph must be constructed by adding either dominating or isolated nodes. Thus, it can be deconstructed iteratively by removing a node of degree zero or a node that connects to the remaining nodes. If this deconstruction failes then the sequence is not a threshold sequence. iiÿÿÿÿi(tsorttpoptlentFalsetTrue(tdegree_sequencetdsR((s<lib/python2.7/site-packages/networkx/algorithms/threshold.pyRs     !c Csº|r|rtdƒ‚nt|tƒrXg|jƒD]\}}||g^q7}n+gt|ƒD]\}}||g^qe}|jƒg}xï|r„|dddkr |jdƒ\}} t|ƒdkrð|jd| dfƒq–|jd| dfƒq–n|ddt|ƒdkr.dS|jƒ\}} |jd| dfƒg|D]}|dd|dg^q]}q–W|r|S|rŸt |ƒSg|D]} | d^q¦S(sæ Determines the creation sequence for the given threshold degree sequence. The creation sequence is a list of single characters 'd' or 'i': 'd' for dominating or 'i' for isolated vertices. Dominating vertices are connected to all vertices present when it is added. The first node added is by convention 'd'. This list can be converted to a string if desired using "".join(cs) If with_labels==True: Returns a list of 2-tuples containing the vertex number and a character 'd' or 'i' which describes the type of vertex. If compact==True: Returns the creation sequence in a compact form that is the number of 'i's and 'd's alternating. Examples: [1,2,2,3] represents d,i,i,d,d,i,i,i [3,1,2] represents d,d,d,i,d,d Notice that the first number is the first vertex to be used for construction and so is always 'd'. with_labels and compact cannot both be True. Returns None if the sequence is not a threshold sequence s#compact sequences cannot be labeleditiRiÿÿÿÿiN( t ValueErrort isinstancetdicttitemst enumerateR R R tinserttNonet make_compact( Rt with_labelstcompacttlabelR RRRtcstv((s<lib/python2.7/site-packages/networkx/algorithms/threshold.pytcreation_sequence3s0 .+  / cCsæ|d}t|tƒr#|}nNt|tƒrRg|D]}|d^q9}nt|tƒre|Stdƒ‚g}d}xUtdt|ƒƒD]>}||||dkr¾|d7}q“|j|ƒd}q“W|j|ƒ|S(sK Returns the creation sequence in a compact form that is the number of 'i's and 'd's alternating. Examples -------- >>> from networkx.algorithms.threshold import make_compact >>> make_compact(['d', 'i', 'i', 'd', 'd', 'i', 'i', 'i']) [1, 2, 2, 3] >>> make_compact(['d', 'd', 'd', 'i', 'd', 'd']) [3, 1, 2] Notice that the first number is the first vertex to be used for construction and so is always 'd'. Labeled creation sequences lose their labels in the compact representation. >>> make_compact([3, 1, 2]) [3, 1, 2] iis"Not a valid creation sequence type(Rtstrttupletintt TypeErrortrangeR tappend(R tfirstRtstccstcountR((s<lib/python2.7/site-packages/networkx/algorithms/threshold.pyRns"        cCs¯|d}t|tƒr|St|tƒr0|St|tƒrI|}n tdƒ‚g}xM|rª|j|jdƒdgƒ|r^|j|jdƒdgƒq^q^W|S(sÍ Converts a compact creation sequence for a threshold graph to a standard creation sequence (unlabeled). If the creation_sequence is already standard, return it. See creation_sequence. is"Not a valid creation sequence typeRR(RR!R"R#R$textendR (R R'tccscopyR((s<lib/python2.7/site-packages/networkx/algorithms/threshold.pyt uncompactšs    $c Cs´|d}t|tƒrAt|tƒr2|}qšt|ƒ}nYt|tƒrpg|D]}|d^qW}n*t|tƒrŽt|ƒ}n tdƒ‚|jƒd}d}xXt|ƒD]J\}}|dkrè|||<|}q½|dkr½|}|d7}q½q½W|jƒxXt|ƒD]J\}}|dkrM|||<|}q"|dkr"|}|d7}q"q"W|dkr‰|d7}ndt |ƒ}g|D]} | |^q S(sö Returns a list of node weights which create the threshold graph designated by the creation sequence. The weights are scaled so that the threshold is 1.0. The order of the nodes is the same as that in the creation sequence. iis"Not a valid creation sequence typeRRgð?( RR!RR"R#R-R$treverseRtfloat( R R'twseqRtwtprevtjR(twscaletww((s<lib/python2.7/site-packages/networkx/algorithms/threshold.pytcreation_sequence_to_weights²s@                ic Cs¡|r|rtdƒ‚nt|tƒrXg|jƒD]\}}||g^q7}n+gt|ƒD]\}}||g^qe}|jƒg}||dd} xº|ra|dd| krí|jdƒ\}}|j|dfƒn7|jƒ\}}|j|dfƒ||dd} t|ƒdkr¨|jƒ\}}|j|dfƒq¨q¨W|j ƒ|rv|S|r†t |ƒSg|D]} | d^qS(sø Returns a creation sequence for a threshold graph determined by the weights and threshold given as input. If the sum of two node weights is greater than the threshold value, an edge is created between these nodes. The creation sequence is a list of single characters 'd' or 'i': 'd' for dominating or 'i' for isolated vertices. Dominating vertices are connected to all vertices present when it is added. The first node added is by convention 'd'. If with_labels==True: Returns a list of 2-tuples containing the vertex number and a character 'd' or 'i' which describes the type of vertex. If compact==True: Returns the creation sequence in a compact form that is the number of 'i's and 'd's alternating. Examples: [1,2,2,3] represents d,i,i,d,d,i,i,i [3,1,2] represents d,d,d,i,d,d Notice that the first number is the first vertex to be used for construction and so is always 'd'. with_labels and compact cannot both be True. s#compact sequences cannot be labelediÿÿÿÿiRRi( RRRRRR R R&R R.R( tweightst thresholdRRRR1R0RRtcutoffR((s<lib/python2.7/site-packages/networkx/algorithms/threshold.pytweights_to_creation_sequenceás0 .+    c Cs"|d}t|tƒr.tt|ƒƒ}nRt|tƒrG|}n9t|tƒrwt|ƒ}tt|ƒƒ}n dGHdStj d|ƒ}|j ƒr°tj dƒ‚nd|_ xb|r|j dƒ\}}|dkr x't|ƒD]}|j||ƒqðWn|j|ƒq¼W|S(sÌ Create a threshold graph from the creation sequence or compact creation_sequence. The input sequence can be a creation sequence (e.g. ['d','i','d','d','d','i']) labeled creation sequence (e.g. [(0,'d'),(2,'d'),(1,'i')]) compact creation sequence (e.g. [2,1,1,2,0]) Use cs=creation_sequence(degree_sequence,labeled=True) to convert a degree sequence to a creation sequence. Returns None if the sequence is not valid is"not a valid creation sequence typesDirected Graph not supportedsThreshold GraphRN(RR!RRR"R#R-Rtnxt empty_grapht is_directedt NetworkXErrortnameR tadd_edgetadd_node( R t create_usingR'tciRR Rt node_typetu((s<lib/python2.7/site-packages/networkx/algorithms/threshold.pytthreshold_graphs*       cCs£xœ|jƒD]Ž\}}x|jƒD]q}|j||ƒ r&||kr&xI|j|ƒD]5}|j||ƒ r[||kr[||||gSq[Wq&q&Wq WtS(s¯ Returns False if there aren't any alternating 4 cycles. Otherwise returns the cycle as [a,b,c,d] where (a,b) and (c,d) are edges and (a,c) and (b,d) are not. (tedgestnodesthas_edget neighborsR(R RERR1tx((s<lib/python2.7/site-packages/networkx/algorithms/threshold.pytfind_alternating_4_cycleQscCstt|ƒ|ƒS(sˆ Return a threshold subgraph that is close to largest in G. The threshold graph will contain the largest degree node in G. (RFtfind_creation_sequence(R RB((s<lib/python2.7/site-packages/networkx/algorithms/threshold.pyR`sc Cs@g}|}x#|jƒdkr1t|jƒƒ}g|jƒD]\}}||f^q@}|jƒ|dddkr®|jt|dgt|ƒddgƒƒPnx@|dddkrð|jdƒ\}}|j |dfƒq±W|jƒ\}}|j |dfƒ|j |j |ƒƒ}qW|j ƒ|S(s… Find a threshold subgraph that is close to largest in G. Returns the labeled creation sequence of that threshold graph. iiÿÿÿÿRiR( torderRR RR R+tzipR R R&tsubgraphRJR.( R RtHtdsdictRRRtisotbigv((s<lib/python2.7/site-packages/networkx/algorithms/threshold.pyRMis"+ . cCs|}|jdƒ}||d|dd}xIt|ƒD];\}}|dkrm|||dd7}q<|d8}q<W|S(sb Compute number of triangles in the threshold graph with the given creation sequence. RiiiR(R*R(R RtdrtntriRttyp((s<lib/python2.7/site-packages/networkx/algorithms/threshold.pyt triangles‰s c Csï|}g}|jdƒ}|d|dd}d}d}x«t|ƒD]\}}|dkr|d7}||d|} nS| dkr¸||d|7}d}||8}d}n|d7}||dd} |j| ƒ|} qJW|S(sT Return triangle sequence for the given threshold graph creation sequence. Riii(R*RR&( R RtseqRUtdcurtiruntdrunRtsymttritprevsym((s<lib/python2.7/site-packages/networkx/algorithms/threshold.pyttriangle_sequences(        cCs—t|ƒ}t|ƒ}g}xrt|ƒD]d\}}||}|dkr`|jdƒq+n||dd}|jt|ƒt|ƒƒq+W|S(sR Return cluster sequence for the given threshold graph creation sequence. iii(R`RRR&R/(R ttriseqtdegseqtcseqRtdegR^tmax_size((s<lib/python2.7/site-packages/networkx/algorithms/threshold.pytcluster_sequence¹s     !cCss|}g}|jdƒ}xQt|ƒD]C\}}|dkr^|d8}|j||ƒq(|j|ƒq(W|S(s] Return degree sequence for the threshold graph with the given creation sequence Ri(R*RR&(R RRYtrdRR]((s<lib/python2.7/site-packages/networkx/algorithms/threshold.pyRÊs  cCs@t|ƒ}tt|ƒƒ}||d}|t|ƒ}|S(s Return the density of the graph with this creation_sequence. The density is the fraction of possible edges present. i(R tsumRR/(R tNttwo_sizet two_possibletden((s<lib/python2.7/site-packages/networkx/algorithms/threshold.pytdensityÛs  cCs”|}d}d}d}d}|jdƒ}gt|ƒD]\}}|dkr:|^q:} t|ƒ} x¾t|ƒD]°\}}|dkrÆ|| dkr¶d|| fGHt‚n| jdƒn| |} xT| D]L} | | } || | 7}|| d| d7}|| | 7}|d7}q×WqwWd||||}d||||}|dkr†|dkrsdStd|ƒ‚n|t|ƒS(s> Return the degree-degree correlation over all edges. iRs!Logic error in degree_correlationiiis$Zero Denominator but Numerator is %s(R*RRRR R/(R Rts1ts2ts3tmRgRR]trdiRtdegitdjtdegjtdenomtnumer((s<lib/python2.7/site-packages/networkx/algorithms/threshold.pytdegree_correlationçs81        c Cs¾|d}t|tƒrKgtt|ƒƒD]}|||f^q,}nrt|tƒrd|}nYt|tƒr±t|ƒ}gtt|ƒƒD]}|||f^q’}n tdƒ‚g|D]}|d^qÄ}||krùtd|ƒ‚n||krtd|ƒ‚n||kr+|gS|j |ƒ} |j |ƒ} t | | ƒ} || ddkrv||gS|| }x7|r¹|j ƒ} | ddkrƒ|| d|gSqƒWdS(s> Find the shortest path between u and v in a threshold graph G with the given creation_sequence. For an unlabeled creation_sequence, the vertices u and v must be integers in (0,len(sequence)) referring to the position of the desired vertices in the sequence. For a labeled creation_sequence, u and v are labels of veritices. Use cs=creation_sequence(degree_sequence,with_labels=True) to convert a degree sequence to a creation sequence. Returns a list of vertices from u to v. Example: if they are neighbors, it returns [u,v] is"Not a valid creation sequence types-Vertex %s not in graph from creation_sequenceiRiÿÿÿÿ( RR!R%R R"R#R-R$RtindextmaxR ( R RERR'RRRCR(tvertstuindextvindextbigindtvert((s<lib/python2.7/site-packages/networkx/algorithms/threshold.pyt shortest_path s6 2  2        cCs•|d}t|tƒrAt|tƒr2|}qÀt|ƒ}nt|tƒr–g|D]}|d^qW}g|D]}|d^qtj|ƒ}n*t|tƒr´t|ƒ}n tdƒ‚t|ƒ}dg|}d||s2  )    cCs=|}g}d}t|jdƒƒ}d}d}d}xµt|ƒD]§\} } | dkr™||d||d|| |||} |d7}n;|dkrÄ| }||8}d}d}nd} |d7}|jt| ƒƒ| }qFW|r9t|ƒ} d| d| d} g|D]}|| ^q }n|S(s¸ Return betweenness for the threshold graph with the given creation sequence. The result is unscaled. To scale the values to the iterval [0,1] divide by (n-1)*(n-2). Rigiigð?(R/R*RR&R (R t normalizedRRYtlastcharRUR[R\tdlastRtctbRNtscaleR(((s<lib/python2.7/site-packages/networkx/algorithms/threshold.pytbetweenness_sequencels2 .        c Cstt|ƒ}t|ƒ}dg|}|}t|ddd…ƒ}|d}dt|ƒg||d`. iisp must be in [0,1]RR(RR%trandomR&(RtptseedRR((s<lib/python2.7/site-packages/networkx/algorithms/threshold.pytrandom_threshold_sequence s cCsºdgdg|d}||kr2d||<|S|||ddkrYtdƒ‚n|d}|d}x.||krd||<|d8}||7}qpW|||}d||<|S(sç Create a skewed threshold graph with a given number of vertices (n) and a given number of edges (m). The routine returns an unlabeled creation sequence for the threshold graph. FIXME: describe algorithm RRiis#Too many edges for this many nodes.(R(RRqRtindRh((s<lib/python2.7/site-packages/networkx/algorithms/threshold.pytright_d_threshold_sequence/s        cCsÉdgdg|d}||kr2d||<|S|||ddkrYtdƒ‚nd||d<|d}d}x.||kr§d||<||7}|d7}qzW||krÅd|||`. iiÿÿÿÿRR(RRžtchoiceR%tremoveR ( Rtp_splitt p_combineR RRDtdlistR¥tsplit_tot flip_sidet first_choicet second_choicettarget((s<lib/python2.7/site-packages/networkx/algorithms/threshold.pytswap_dts(8 ,    .   (&t__doc__tmathRtnetworkxR;tnetworkx.utilsRt__all__RRRR RR-R6R:RRFRLRRMRXR`RfRRmRxR€R‚RR‰R‘R˜RR¡R£R¤R¯(((s<lib/python2.7/site-packages/networkx/algorithms/threshold.pyt sB    ; ,  /= 3      " 5 . ( :  ) " " #