# HOTnet-maps

Model was written in NetLogo 5.0.3
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extensions [ gis ] globals [ cities-dataset countries-dataset citiesVectorFeature ] breed [ cities city ] ;; the number of hops from a fixed center of the tree cities-own [ nhop ] ;;;;;;;;;;;;;;;;;;;;;;;; ;;; Setup Procedures ;;; ;;;;;;;;;;;;;;;;;;;;;;;; to setup clear-all ; Note that setting the coordinate system here is optional, as ; long as all of your datasets use the same coordinate system. gis:load-coordinate-system (word "data/" projection ".prj") ; Load all of our datasets set cities-dataset gis:load-dataset "data/cities/cities.shp" ;set cities-dataset gis:load-dataset "data/cities.shp" set countries-dataset gis:load-dataset "data/countries.shp" ;; Set the world envelope to the union of all of our dataset's envelopes gis:set-world-envelope (gis:envelope-union-of (gis:envelope-of cities-dataset) (gis:envelope-of countries-dataset)) ;; Display countries gis:set-drawing-color white gis:draw countries-dataset 1 ;; list of cities represented by VectorFeature ordered by country ;set citiesVectorFeature sort-by [gis:property-value ?1 "CNTRY_NAME" > gis:property-value ?2 "CNTRY_NAME"] gis:feature-list-of cities-dataset ;set citiesVectorFeature sort-by [gis:property-value ?1 "COUNTRY" > gis:property-value ?2 "COUNTRY"] gis:feature-list-of cities-dataset ;; list of cities represented by VectorFeature in a random order set citiesVectorFeature shuffle gis:feature-list-of cities-dataset set-default-shape cities "circle" ;; create first 2 cities connected by a backbone create-cities 1 [ let location gis:location-of (first (first (gis:vertex-lists-of item 0 citiesVectorFeature))) setxy item 0 location item 1 location set size 1 ;; set color of the city proportionally with population: darker = bigger set color scale-color red (gis:property-value item 0 citiesVectorFeature "POP_RANK") 1 7 ;set color scale-color red (gis:property-value item 0 citiesVectorFeature "POPULATION") 5000000 1000 set nhop 0 ] create-cities 1 [ let location gis:location-of (first (first (gis:vertex-lists-of item 1 citiesVectorFeature))) setxy item 0 location item 1 location set size 1 ;; set color of the city proportionally with population: darker = bigger set color scale-color red (gis:property-value item 1 citiesVectorFeature "POP_RANK") 1 7 ;set color scale-color red (gis:property-value item 0 citiesVectorFeature "POPULATION") 5000000 1000 create-link-with turtle 0 [ set color green ] set nhop 1 ] reset-ticks end ;;;;;;;;;;;;;;;;;;;;;;; ;;; Main Procedures ;;; ;;;;;;;;;;;;;;;;;;;;;;; to go if (ticks + 2) = length citiesVectorFeature [ stop ] ;; new edge is green, old edges are gray ask links [ set color gray ] ;; index of the list cities let current-city item (ticks + 2) citiesVectorFeature ; a feature in a point dataset may have multiple points, so we ; have a list of lists of points, which is why we need to use ; first twice here let location gis:location-of (first (first (gis:vertex-lists-of current-city))) ; location will be an empty list if the point lies outside the ; bounds of the current NetLogo world, as defined by our current ; coordinate transformation if not empty? location [ ;; The behavior of the model depends crucially on the value of alfa: ;; if alfa is less than a particular constant depending on the shape of the region, ;; then Euclidean distances are not important, and the resulting network is easily seen to be a star, ;; the ultimate in degree concentration, and, depending on how you look at it, the exact opposite, or absurd extreme, of a power law. ;; If alfa grows at least as fast as sqrt(n), where n is the final number of points, then Euclidean distance becomes too important, ;; and the resulting graph is a dynamic version of the Euclidean minimum spanning tree, in which high degrees do occur, ;; but with exponentially vanishing probability. ;; If, however, alfa is anywhere in between — is larger than a certain constant, but grows slower than sqrt(n) if at all — ;; then, almost certainly, the degrees obey a power law. let x item 0 location let y item 1 location let partner nobody ;; Node i attaches itself to the node j that minimizes the weighted sum of the two objectives: ;; alfa * dij + hj ;; where dij is the /normalized/ Euclidean distance, and hj is some measure of the “centrality” of node j, such as ;; (a) the average number of hops from other nodes; ;; (b) the maximum number of hops from another node; ;; (c) the number of hops from a fixed center of the tree; ;; all three measures result in similar power laws. ;; We use metric (b). To compute it we choose tourtle 0 as the center of our network. Then the maximum number of hops from a node is: ;; number of hops of the node from the center + maximum number of hops a node is from the center. ;; we must check the case when nodes with maximum number of hop are children of current node to don't overstimate hj by an excess of max_nhop - 1 ;; Optionally there is a preference to attach to bigger city set partner min-one-of cities [ alfa * sqrt ( ;;( (x - min-pxcor + 0.5) / (max-pxcor - min-pxcor) - (xcor - min-pxcor + 0.5) / (max-pxcor - min-pxcor) ) ^ 2 + ( (x - xcor) / (max-pxcor - min-pxcor) ) ^ 2 + ;;( (y - min-pycor + 0.5) / (max-pycor - min-pycor) - (ycor - min-pycor + 0.5) / (max-pycor - min-pycor) ) ^ 2 ( (y - ycor) / (max-pycor - min-pycor) ) ^ 2 ) + hj self + ifelse-value (city_size_pref? and gis:property-value current-city "POP_RANK" > 0) ;+ ifelse-value (city_size_pref? and gis:property-value current-city "POPULATION" > 0) ;; the greater is the city the less is the added value ;; 7 less than 50K ;; 6 50K < people < 100K ;; 5 100K < people < 250K ;; 4 250K < people < 500K ;; 3 500K < people < 1M ;; 2 1M < people < 5M ;; 1 greater than 5M [ gis:property-value current-city "POP_RANK" ] [0] ] if partner != nobody [ create-cities 1 [ setxy x y set size 1 ;; set color of the city proportionally with population: darker = bigger set color scale-color red (gis:property-value current-city "POP_RANK") 1 7 ;set color scale-color red (gis:property-value current-city "POPULATION") 5000000 1000 create-link-with partner [ set color green ] set nhop 1 + [ nhop ] of partner ] ] ] ;; END if not empty? location tick end ;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;; Compute hj heuristic ;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;; to-report hj [node] let max_nhop max [nhop] of cities ;; if all cities at max_nhop are children of current-city then decrease hj while [ all? cities with [nhop = max_nhop] [ is-child node max_nhop] ] [ set max_nhop max_nhop - 1 ] report max_nhop + [nhop] of node end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;; Find if city at max_ops is child of current-city ;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to-report is-child [root max-nhop] let child false if root != city 0 ;; all cities are children of the root of the tree, so don't check it! [ ask root [ ask link-neighbors with [nhop > [nhop] of root] [ ifelse nhop = max-nhop [ set child true ] [ set child is-child self max-nhop] ;; use of recursion to traverse the tree ] ] ] report child end ;;;;;;;;;;;;;;;;;;;; ;;; Compute s(g) ;;; ;;;;;;;;;;;;;;;;;;;; to-report log-likelihood let s 0 ;; for each link compute di*dj and sum it to s ask links [ set s s + [ count link-neighbors ] of end1 * [ count link-neighbors ] of end2 ] report s end ;;;;;;;;;;;;;;;;;;;;;;;; ;;; Compute S-metric ;;; ;;;;;;;;;;;;;;;;;;;;;;;; to-report relative-log-likelihood let smax 0 let counter 0 let di 0 let child 0 ;; D = { d1, d2, d3, ..., dn }, d1 >= d2 >= d3 >= ... >= dn let degree-sequence sort-by > [ count link-neighbors ] of turtles set di item 0 degree-sequence set degree-sequence remove-item 0 degree-sequence foreach degree-sequence [ set smax smax + di * ? set counter counter + 1 if di = counter ;; we have iterated through all di's childs; if di = 0 select the highest degree. [ set counter 1 ;; count the parent if it's not the root set di item child degree-sequence ;; select child; child = 0 is the root. set child child + 1 ] ] report log-likelihood / smax end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;; Save Nodes Degrees to file ;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to save-node-degree-to-file if file-exists? "NodeDegrees.txt" [ file-delete "NodeDegrees.txt" ] file-open "NodesDegrees.txt" ;; save in descending orders ;; D = { d1, d2, d3, ..., dn }, d1 >= d2 >= d3 >= ... >= dn foreach sort-by > [ count link-neighbors ] of turtles [ file-print ? ] file-close end ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ;;; Export Graph Connectivity to txt ;;; ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; to export-graph if file-exists? "HOTGraph.txt" [ file-delete "HOTGraph.txt" ] file-open "HOTGraph.txt" ;; write each linked couple of tourtles and their degree ask links [ file-type [who] of end1 ;; writes without blank spaces file-write [who] of end2 ;; write a space value space file-print "" ;; write carriage return ] file-close end ;;;;;;;;;;;;;; ;;; Layout ;;; ;;;;;;;;;;;;;; ;; resize-nodes, change back and forth from size based on degree to a size of 1 to resize-nodes ifelse all? turtles [size = 1] [ ;; a node is a circle with diameter determined by ;; the SIZE variable; using SQRT makes the circle's ;; area proportional to its degree ask turtles [ set size sqrt count link-neighbors ] ] [ ask turtles [ set size 1 ] ] end ; Copyright 2013 Tomasini Marcello. ; See Info tab for full copyright and license.

There is only one version of this model, created almost 8 years ago by Marcello Tomasini.

## Attached files

File | Type | Description | Last updated | |
---|---|---|---|---|

data.zip | data | GIS dataset | almost 8 years ago, by Marcello Tomasini | Download |

HOTnet-maps.png | preview | model view | almost 8 years ago, by Marcello Tomasini | Download |

**Parent:** HOTnet

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