Metanet User's Guide and Tutorial
Contents
1. 1 2 Various representations of graphs 1 2 1 Names and numbers Las Talhead gt o ee ei aue ee 1 2 3 Adjacency lists 1 2 4 Node arc matrix 1 2 5 Node node matrix 1 2 6 Chained lists 2 424054 2 Managing graphs 2 1 Creating graphs 2 2 Loading and saving graphs 2 3 Plotting graphs 1 0 6d ve eee 3 Metanet windows 3 1 Using the Metanet window S Al Begin mod 2 rede a 2 3 1 2 Studymode 4 4848 3 1 3 Modifymode 3 2 Using the Metanet window from Scilab_ 3 2 1 Showing a graph 3 2 2 Showing arcs and nodes 3 2 3 Managing Metanet windows 3 2 4 Synchronism 4 Generating graphs and networks 5 Computations on graphs and networks 5 1 Graph manipulations and transformations 5 2 Graphcomputations 5 3 Network computations 5 4 Other computations List of Figures 1 Small directed graph 2 Chained lists representation of graphs 3 Smallest directed graph 4 Small undirected graph 5 Directed graph o o e se es A ae 19 10 11 11 11 12 12 14 14 14 15 15 152. 3 Metanet windows Metanet windows can be used to see the graphs and the networks Itis a powerful tool to create and modify graphs You can have as many Metanet windows as you want at the same time Each Metanet window is an Unix process the communications between Scilab and the Metanet windows is made by using the communication toolbox called GeCI NOTE that at the present time Metanet windows only work under Unix environment with X Window By default the size of Metanet windows is 1000 pixels by 1000 pixels If you want to see big graphs you have to change this values by using X Window ressources Put the new values in the res sources Metanet drawWidth and Metanet drawHeight in a standard ressource file for in stance Xdefaults in your home directory For instance if you want Metanet windows with a size of 2000 by 3000 pixels puts the following lines in the ressource file Metanet drawWidth 2000 Metanet drawHeight 3000 An important point is that there is no link between the graph displayed in the Metanet window and the graphs loaded into Scilab So when you have created or modified a graph in the Metanet window you have to save it as a graph file see 2 2 and load it again in Scilab Conversely when you have modified a graph in Scilab you have to display it again in the Metanet window by using the save_graph function see 3 2 The philosophy is that computations are only made in Scilab and the Metanet window is only used to displa
3. node or the number of an edge we mean the internal number 1 2 2 Tail head We have seen that the standard representation of a graph used by Metanet is by the means of two row vectors tail and head arc number i goes from node number tail i to node number head i The size of these vectors is the same and is the number of arcs of the graph Moreover the number of nodes must be given It is greater than or equal to the maximum integer number in tail and head If node numbers do not belong to tail and head then there are isolated nodes If the graph is undirected it is the same but tail i and head i can be exchanged This representation is very general and gives directed or undirected multigraphs with possible loops and isolated nodes Figure 1 Small directed graph The standard function to create graphs is make_graph see 2 1 For instance we can create a small directed graph with a loop and an isolated node see figure 1 by using node number 4 tail 1 1 2 3 head 2 3 1 3 or in Scilab g make_graph foo 1 4 11 2 3 2 3 1 3 1 2 3 Adjacency lists Another interesting representation often used by algorithms is the adjacency lists representation It uses three row vectors 1p 1s and la If n is the number of nodes and m is the number of arcs of the graph lp is the pointer array size n 1 1s is the node array size m la is the arc array size m If the graph is undirected each edge corres
4. to obtain the chained lists representation of a graph from the adjacency lists representation see 1 2 3 2 Managing graphs We have seen see 1 1 that a graph in Scilab is represented by a graph list This list contains everything needed to define the graph arcs nodes coordinates colors attributes width of the arcs etc To create load and save graphs in Scilab you can use only Scilab functions handling graph lists or you can use the Metanet window We describe here the first way For the second way see 3 2 1 Creating graphs The standard function for making a graph list is make_graph The first argument is the name of the graph the second argument is a flag which can be 1 directed graph or O undirected graph the third argument is the number of nodes of the graph and the last two arguments are the tail and head vectors of the graph We have already seen that the graph named foo in figure 1 can be created by the command g make_graph foo 1 4 1 1 2 3 2 3 1 3 The simplest graph we can create in Metanet is g make_graph min 1 1 1 1 It is directed has one node and one loop arc on this node and can be seen in figure 3 The following graph shown in figure 4 is the same as the first graph we have created but it is undir ected g make_graph ufoo 0 4 1 1 2 3 2 3 1 3 Figure 5 Directed graph You can also give 0 as the third argument of make_graph number of nodes This mea
5. Metanet User s Guide and Tutorial Claude Gomez Maurice Goursat Manual version 1 1 for Scilab 2 4 Metanet is a toolbox of Scilab for graphs and networks computations It comes as new Scilab func tions together with a graphical window for displaying and modifying graphs You can use the Metanet toolbox in Scilab without using the graphical window window at all i e without seeing the graphs or the networks you are working with 1 Representation of graphs The graphs handled by Metanet are directed or undirected multigraphs loops are allowed A graph is a set of arcs and nodes A graph must have at least one arc We call arc a directed link between two nodes For instance the arc i j goes from tail node i to head node j We call edge the corresponding undirected link A minimal way to represent a graph is to give the number of nodes the list of the tail nodes and the list of the head nodes Each node has a number and each arc has a number The numbers of nodes are consecutive and the number of arcs are consecutive In Scilab these lists are represented by row vectors So if we call tail and head these row vectors the arc number 7 goes from node number t ail i to node number head i Moreover it is necessary to give the number of nodes because isolated nodes without any arc can exist The size of the vectors t ail and head is the number of edges of the graph This is the standard representation of graphs in Metanet as it is describ
6. Save Save the modified graph in the default directory All the arcs and nodes must have names Save As Save the modified graph with a new name in the default directory All the arcs and nodes must have names Quit Exit Modify Mode If the graph has been modified it must be saved first Graph Characteristics If there is an highlighted arc or node print its characteristics otherwise print the characteristics of the graph Find Arc Prompt for an arc name and highlight it The viewport of the window is moved to display the arc if needed Find Node Prompt for a node name and highlight it The viewport of the window is moved to display the arc if needed Graphics Change the scale The default is 1 Use internal numbers as names Use the consecutive internal numbers of arcs and nodes as names This is useful when doing computations with Scilab Display arc names Display arc names on the arcs Display node names Display node names on the nodes Modify Attributes Display the attributes of the highlighted arc or node Then they can be changed Delete Delete the highlighted arc or node NOTE there is no undelete Name Name the highlighted arc or node Color Give a color to the highlighted arc or node Create Loop Create a loop arc on the highlighted node Create Sink Transform the highlighted node into a sink Create Source Transform the highlighted node into a source Remove Sink Source Transform the highlighted source or sink
7. ail and head cannot be empty For instance you can define a graph list see 2 1 by g make_graph min 1 1 1 1 which is the simplest graph you can create it is directed has one node and one loop arc on this node Each element of the list can be accessed by using its name For instance if g is a graph list and you want to get the node_number element you only have to type g node_number and if you want to change this value to 10 you only have to type g node_number 10 The check_graph function checks a graph list to see if there are inconsistencies in its elements Checking is not only syntactic number of elements of the list compatible sizes of the vectors but also semantic in the sense that check_graph checks that node_number tail and head elements of the list can really represent a graph This checking is automatically made when calling functions with a graph list as an argument You will find below the description of all the elements of a graph list Each element is described by one or more lines The first lines give the name of the element and its definition with its Scilab type if needed The last line gives the default for elements that can have one The name of the element is used to access the elements of the list name Name of the graph a string with a maximum of 80 characters REQUIRED directed Flag giving the type of the graph it is equal to 1 if the graph is directed or equal to O is the g
8. ected node to a graph arc_graph graph with nodes corresponding to arcs arc_number number of arcs of a graph contract_edge contracts edges between two nodes delete_arcs deletes all the arcs or edges between a set of nodes delete_nodes deletes nodes edge_number number of edges of a graph graph_2_mat node arc or node node matrix of a graph graph_simp converts a graph to a simple undirected graph graph_sum sum of two graphs graph_union union of two graphs line_graph graph with nodes corresponding to edges mat_2_graph graph from node arc or node node matrix node_number number of nodes of a graph nodes_2_path path from a set of nodes path_2_nodes set of nodes from a path split_edge splits an edge by inserting a node subgraph subgraph of a graph supernode replaces a group of nodes with a single node 5 2 Graph computations These functions are used to make standard computations on graphs articul finds one or more articulation points best_match best matching of a graph circuit finds a circuit or the rank function in a directed graph con_nodes set of nodes of a connected component connex connected components 16 cycle_basis basis of cycle of a simple undirected graph find_path finds a path between two nodes girth girth of a directed graph graph_center center of a graph graph_complement complement of a graph graph_diameter diameter of a graph graph_power kth power of a directed 1 graph hamilton hamiltonian circuit of a graph
9. ed in the graph list see 1 1 There are functions to compute other representations better suited for some algorithms see 1 2 The distinction between edges and arcs is meaningful when we deal with undirected graphs This distinction is not needed when we only use the standard functions of Metanet There is no distinction between an arc and a directed edge We will often use indistinctly these two terms A new object the graph list data structure is defined in Scilab to handle graph It is described below 1 1 The graph list data structure Metanet uses the graph list data structure to represent graphs With this type of description see 1 2 we can have directed or undirected multigraphs and multiple loops are allowed The graph list data structure is a typed list As usual the first element of this object is itself a list which defines its type graph and all the access functions to the other elements The graph list has 33 elements not counting the first one defining the type Only the first five elements must have a value in the list all the others can be given the empty vector as a value and then a default is used These five required elements are name name of the graph a string directed flag equal to 1 if the graph is directed or equal to 0 if the graph is undirected node_number number of nodes tail row vector of the tail node numbers head row vector of the head node numbers A graph must at least have one arc so t
10. ere is one arc from node to node j Only 1 to 1 graphs no more than one arc from one node to another can be represented but loops are allowed This matrix is also known as the adjacency matrix The same functions used to compute the node are matrix see above of a graph are used to compute the node node matrix graph_2_mat and mat_2_graph To specify that we are working with the node node matrix the flag nodenode must be given as the last argument of these functions For instance you can find below the node node matrix of the graph corresponding to Figure 1 0 11 0 1 0 0 0 0 0 1 0 0 0 0 0 and the node node matrix for the same undirected graph Corr oO oo oOo Cor OF So 1 2 6 Chained lists Another representation used by some algorithms is given by the chained lists This representation uses four vectors fe che fn and chn which are described below e1 fe i is the number of the first edge starting from node i e2 che e1 is the number of the second edge starting from node i e3 che e2 is the number of the third edge starting from node i and so on until the value is 0 fn i is the number of the first node reached from node i chn i is the number of the node reached by edge che i e2 che el e3 che e2 Figure 2 Chained lists representation of graphs 1 oy Figure 3 Smallest directed graph All this can be more clearly seen on figure 2 You can use the chain_struct function
11. h Default is 3 default_font_size Default size of the font used to draw the names or the labels of nodes and edges Default is 12 node_label Row vector of the node labels Node labels are used to draw a string in a node It can be any string An empty label can be given as a blank string edge_label Row vector of the edge labels Edge labels are used to draw a string on an edge It can be any string An empty label can be given as a blank string 1 2 Various representations of graphs 1 2 1 Names and numbers First of all we need to distinguish between the name of a node or the name of an edge and their internal numbers The name can be any string Its is saved in the graph file see 2 2 The internal number is generated automatically when loading a graph The nodes and the edges have consecutive internal numbers starting from 1 When using the Scilab functions working on graphs all the computations are made with internal numbers It is very important to give different names to the nodes because the nodes are distinguished by their names when they are loaded This distinction is not important for edges Often the names are taken as the internal numbers This is the default when no names are given In this case the distinction between a name and a number is not meaningful Only the type of the variable is not the same the name is a string and the number is an integer In the following when we talk about the number of a
12. indows to terminate This mode is the most efficient But when running a lots of graphics commands problems can arise For instance you might highlight a set of nodes in a bad Metanet window because the good one has not yet appeared So it is possible to use a synchronous mode Then Scilab waits until the functions dealing with the Metanet windows have terminated The met anet_sync function is used to change the mode met anet_sync 0 changes to asyn chronous mode default met anet_sync 1 changes to synchronous mode and met anet sync returns the current mode 0 asynchronous 1 synchronous 4 Generating graphs and networks When working with graphs and particularly with networks it is very useful to generate them automatic ally The function gen_net can be used in Metanet to generate networks It uses a triangulation method for generating a planar connected graph and then uses the information of the user to give arcs and nodes good values of costs and capacities 5 Computations on graphs and networks Most functions of the Metanet toolbox are used to make computations on graphs and networks We can distinguish four classes of such functions and we will describe them briefly For more information see the on line help 15 5 1 Graph manipulations and transformations You can use these functions to get information about graphs or to modify existing graphs add_edge adds an edge or an arc between two nodes add_node adds a disconn
13. is_connex connectivity test max_clique maximum clique of a graph min_weight_tree minimum weight spanning tree neighbors nodes connected to a node nodes_degrees degrees of the nodes of a graph perfect_match min cost perfect matching predecessors tail nodes of incoming arcs of a node shortest_path shortest path strong_con_nodes set of nodes of a strong connected component strong_connex strong connected components successors head nodes of outgoing arcs of a node trans_closure transitive closure 5 3 Network computations These functions make computations on networks This means that the graph has capacities and or costs values on the edges max_cap_path maximum capacity path max_flow maximum flow between two nodes min_Icost_cflow minimum linear cost constrained flow min_Icost_flow1 minimum linear cost flow min_Icost_flow2 minimum linear cost flow min_qcost_flow minimum quadratic cost flow pipe_network pipe network problem 17 5 4 Other computations These functions do not make computations directly on graphs and networks but they have strong links with them bandwr bandwidth reduction for a sparse matrix convex_hull convex hull of a set of points in the plane knapsack solves a 0 1 multiple knapsack problem mesh2d triangulation of n points in the plane qassign solves a quadratic assignment problem salesman solves the travelling salesman problem 18 Contents 1 Representation of graphs 1 1 The graph list data structure
14. node into a plain node It has no effect if the highlighted node is neither a source nor a sink Automatic Name Give the consecutive internal arc and node numbers as the names of arcs and nodes This can be useful for a new graph NOTE that if some arcs and nodes already have names they are replaced by the corresponding internal numbers Default Values Change some default values e the default size of the font e the default diameter of the nodes 13 e the default width of the border of the nodes e the default width of the arcs e the default width of the highlighted arcs Redraw Refresh the screen and redraw the graph 3 2 Using the Metanet window from Scilab The standard way of using the Metanet window is from Scilab Indeed the Metanet window is opened only when needed as a new process Many Metanet windows can be opened at the same time Each Metanet window has a number integer starting from 1 One of these windows is the current Metanet window The met anet function opens a new Metanet window and returns its number A path can be given as an optional argument it is the directory where graph files are searched by default graph files are searched in the working directory The met anet function is mainly used when we want to create a new graph We describe below the Scilab functions used in conjunction with the Metanet window 3 2 1 Showing a graph The first thing we would like to do is to see the graph we are working with
15. ns that make_graph will compute itself from its last arguments the tail and head vectors the number of nodes of the graph So this graph has no isolated node and the nodes names are taken from the numbers in tail and head vectors For instance if you enter g make_graph fool 1 0 1 1 4 3 4 3 1 3 the graph shown in figure 5 has three nodes with names 1 3 and 4 no isolated node and four edges Note the difference with the graph of figure 1 The other elements of the graph list see 1 1 can be entered by using the names of the elements For instance to give graph foo coordinates for the nodes you can enter g make_graph foo 1 4 11 2 3 2 3 1 3 g node_x 42 108 176 162 g node_y 36 134 36 93 Another simple example if you want to transform the directed graph g into an undirected graph you only have to do g directed 0 There is a wizard way to create a graph list by hands without using the make_graph function This can be useful when writing your own Scilab functions You can use the Scilab function glist which must have as many arguments as the elements of the graph list see 1 1 This way can lead to errors because the list is somehow long You can use the check_graph function to check if the graph list is correct 2 2 Loading and saving graphs Graphs are saved in ASCII files called graph files A graph file has the extension graph The structure of a gra
16. ode_border Row vector of the sizes of the node borders in pixels Default is the value of element default_node_border node_font_size Row vector of the sizes of the font used to draw the name or the label of the node you can choose 8 10 12 14 18 or 24 Default is the value of element default_font _size node_demand Row vector of the node demands The demands of the nodes are used in functions min_lcost_cflow min_lcost_flowl min_lcost_flow2 min_qcost_flow and supernode Default is 0 edge_name Row vector of the edge names edge names need not be different Default is the edge numbers as edge names edge_color Row vector of the edge colors the color is an integer from 0 to 16 see node_color Default is 0 black edge_width Row vector of the sizes of the edge widths in pixels Default is the value of element default_edge_width edge_hi_width Row vector of the sizes of the highlighted edge widths in pixels Default is the value of element default_edge_hi_width edge_font_size Row vector of the sizes of the font used to draw the name or the label of the edge you can choose 8 10 12 14 18 or 24 Default is the value of element default_font _size edge_tength Row vector of the edge lengths The lengths of the edges are used in functions graph_center graph_diameter salesman and shortest_path Default is 0 edge_cost Row vector of the edge costs The costs of the edges are used in functions min_lcost_cflow min_lc
17. ost_flowl andmin_lcost_flow2 Default is 0 edge_min_cap Row vector of the edge minimum capacities The minimum capacities of the edges are used in functions max_flow min_lcost _cflow min_lcost_flowl1 min_lcost_flow2 and min_qcost_flow Default is 0 edge_max_cap Row vector of the edge maximum capacities The maximum capacities of the edges are used in functions max_cap_path max_flow min_lcost_cflow min_lcost_flowl min_lcost_flow2 and min_qcost _flow Default is 0 edge_q_weight Row vector of the edge quadratic weights It corresponds to w u in the value of the cost on edge u with flow y u w u p u wo u The quadratic weights of the edges are used in function min_qcost_flow Default is 0 edge_q_orig Row vector of the edge quadratic origins It corresponds to wo u in the value of the cost on edge u with flow y u 4w u y u wo u The quadratic origins of the edges are used in function min_qcost_flow Default is 0 edge_weight Row vector of the edge weights The weights of the edges are used in function min_weight_tree Default is 0 default_node_diam Default size in pixels of the node diameters of the graph Default is 20 default_node_border Default size in pixels of the node borders of the graph Default is 2 default_edge_width Default size in pixels of the edge widths of the graph Default is 1 default_edge_hi_width Default size in pixels of the highlighted edge widths of the grap
18. ph file is given below j Q RAPH TYPE 0 UNDIRECTED 1 DIRECTED DEFAULTS NODE DIAME ER NODE BORDE first line continuing ARC WIDTH HILITED ARC WIDTH FONTSIZE one line with above values gt UMBER OF ARCS one line with the number of arcs gt UMBER OF NODES one line with the number of nodes gt kkkkkk kxk k k k kx xx x x x x xx xk x x x kx k k ESCRIPTION OF ARCS RC NAME TAIL NODE NAME HEAD NODE NAME COLOR WIDTH HIWIDTH FONTSIZI COST MIN CAP CAP MAX CAP LENGTH Q WEIGHT Q ORIGIN WEIGHT lt one blank line gt lt two lines for each arc gt KKK KKK KKK KKK KKK KKK KKK KKK KKK KKK KKK KKK KKKK DESCRIPTION OF NODES NODE NAME POSSIBLE TYPE 1 SINK 2 SOURCI X Y COLOR DIAMETER BORDER FONTSIZE DEMAND lt one blank line gt lt three lines for each node gt PU A ZAZA Gl Gl T H For an undirected graph ARC is replaced by EDGE Moreover the values of NODE DIAMETER NODE BORDER ARC WIDTH HILITED ARC WIDTH and FONTSIZE for the graph COLOR WIDTH HIWIDTH and FONTSIZE for the arcs and POSSIBLE TYPE COLOR DIAMETER BORDER and FONTSIZE for the nodes can be omitted or equal to 0 then the default is used see 1 1 It is possible to c
19. ponds to two arcs With this type of representation it is easy to know the successors of a node Node number i has lp i 1 1p i successors nodes with numbers from 1s lp i to 1s 1lp it 1 1 the cor responding arcs are have numbers from la lp i tola lp itl 1 The adjacency lists representation of the graph of figure 1 is given below 1 2 3 4 5 The function used to compute the adjacency list representation of a graph is adj_lists 1 2 4 Node arc matrix For a directed graph if n is the number of nodes and m is the number of arcs of the graph the node are matrix A isan x m matrix if A i j 1 then node 7 is the tail of arc 7 if A i j 1 then node 7 is the head of arc i If the graph is undirected and m is the number of edges the node arc matrix A is also a n x m matrix and if A i 7 1 then node 2 is an end of edge j With this type of representation it is impossible to have loops This matrix is represented in Scilab as a sparse matrix For instance the node arc matrix corresponding to figure 1 with loop arc number 4 deleted is 1 1 1 1 0 1 0 1 0 0 0 0 If the same graph is undirected the matrix is 1 11 1 0 1 010 000 The functions used to compute the node arc matrix of a graph and to come back to a graph from the node arc matrix are graph_2_mat and mat_2_graph 1 2 5 Node node matrix The n x n node node matrix of the graph is the matrix A where A i 7 1 if th
20. raph is undirected REQUIRED node_number Number of nodes REQUIRED tail Row vector of the tail node numbers REQUIRED head Row vector of the head node numbers REQUIRED node_name Row vector of the node names they MUST be different Default is the node numbers as node names node_type Row vector of the node types the type is an integer from 0 to 2 0 plain node 1 sink node 2 source node This element is mainly used to draw the nodes in the Metanet window A plain node is drawn as a circle A sink or source node is a node where extraneous flow goes out the node or goes into the node it is drawn differently a circle with an outgoing or ingoing arrow Default is 0 plain node node_x Row vector of the x coordinates of the nodes Default is computed when showing the graph in the Metanet window see 3 node_y Row vector of the y coordinates of the nodes Default is computed when showing the graph in the Metanet window see 3 node_color Row vector of the node colors the color is an integer from 0 to 16 j black navyblue blue skyblue aquamarine forestgreen green lightcyan cyan orange gt red Magenta N violet W yellow is gold Nn beige 16 white Default is 0 black node_diam Row vector of the sizes of the node diameters in pixels a node is drawn as a circle Default is the value of element default_node_diam n
21. reate by hands a graph file and to load it into Scilab but it is a very cumbersome job Programs are given to generate graphs see 4 To load a graph into Scilab use the Load_graph function Its argument is the absolute or relative pathname of the graph file if the graph extension is missing it is assumed load_graph returns the corresponding graph list For instance to load the graph foo which is in the current directory and put the corresponding graph list in the Scilab variable g do g load_graph foo or g load_graph foo graph To load the graph mesh100 given in the Scilab distribution do g load_graph SCI demos metanet mesh100 graph To save a graph use the save_graph function Its first argument is the graph list and its second argument is the name or the pathname of the graph file if the graph extension is missing it is assumed If the path is the name of a directory the name of the graph is used as the name of the file For instance the following command saves the graph g into the graph file foo graph save_graph g foo graph 2 3 Plotting graphs The fastest way to see a graph is to plot it in a Scilab graphical window We can use the plot_graph function to do this Note that no interaction is possible with the displayed graph If you want to graphic ally modify the graph use Metanet windows see 3 10
22. urrent Metanet window By default using one of these functions switch off any preceeding highlighting If you want to keep preceeding highlighting use the optional argument sup For instance the following commands displays the graph g and highlights 3 arcs and 2 nodes show_graph g show_arcs 1 10 3 show_nodes 2 7 sup 14 Note that another way to distinguish arcs and nodes in a displayed graph is to give them colors For that you have to use the elements edge_color and node_color of the graph list see 1 1 But you have to modify the graph list of the graph and use show_graph again to display the graph with the new colors 3 2 3 Managing Metanet windows The net window function is used to change the current Metanet window For instance net window 2 chooses Metanet window number 2 as the current Metanet window The netwindows function returns a list Its first element is the row vector of all the Metanet windows numbers and the second element is the number of the current Metanet window This number is equal to 0 if no current Metanet window exists In the following example there are two Metanet windows with numbers 1 and 3 and the Metanet window number 3 is the current Metanet window gt netwindows ans ans 1 I Zal ans 2 3 3 2 4 Synchronism By default Metanet windows work with Scilab in asynchronous mode i e Scilab proceeds without wait ing for graphics commands sent to Metanet w
23. use the show_graph function show_graph g displays the graph g in the current Metanet window If there is no current Metanet window a new Metanet window is created and it becomes the current Metanet window If there is already a graph displayed in the current Metanet window the new graph is displayed instead The number of the current Metanet window where the graph is displayed is returned by show_graph Two optional arguments can be given to show_graph g after the graph list If an optional ar gument is equal to the string new a new Metanet window is created If an optional argument is a positive number it is the value of the scale factor when drawing the graph see 3 1 For instance show_ graph g new 2 displays the graph g in a new Metanet window with the scale factor equal to 2 3 2 2 Showing arcs and nodes Another very useful thing to do is to distinguish a set of nodes and or a set of arcs in the displayed graph This is done by highlighting nodes and or arcs use the show_arcs and show_nodes functions The arguments of the show_arcs and show_nodes functions are respectively a row vector of arc numbers or edge numbers if the graph is undirected or a row vector of node numbers These sets of arcs and nodes are highlighted in the current Metanet window Note that the corresponding graph must be displayed in this window otherwise the numbers might not correspond to arcs or nodes numbers see 3 2 3 for changing the c
24. ve to choose one Directory Change the default directory Save As Save the loaded graph with a new name in the default directory Quit Quit Metanet Graph Characteristics If there is an highlighted arc or node print its characteristics otherwise print the characteristics of the graph Find Arc Prompt for an arc name and highlight it The viewport of the window is moved to display the arc if needed Find Node Prompt for a node name and highlight it The viewport of the window is moved to display the arc if needed Graphics Change the scale The default is 1 Modify Graph Enter Modify mode Use internal numbers as names Use the consecutive internal numbers of arcs and nodes as names This is useful when doing computations with Scilab Display arc names Display arc names on the arcs Display node names Display node names on the nodes Redraw Refresh the screen and redraw the graph 3 1 3 Modify mode In this mode you can modify and save the graph With the left button of the mouse you can highlight an arc or a node With the right button of the mouse you can modify the graph e if you click where there is no arc or node a new node is created 12 if you click on a node and another node is highlighted a new arc is created between the two nodes if you click on a node and drag the mouse the node is moved You will find below the description of the items of the menus Files Directory Change the default directory
25. y create or modify graphs So you can use Metanet toolbox without using Metanet windows Another way to see a graph is to plot it in a Scilab graphical window see 2 3 but there is no possibility to modify the displayed graph 3 1 Using the Metanet window To open a Metanet window use the metanet or show_graph Scilab functions see 3 2 The Metanet window comes with three modes When no graph is loaded you are in the Begin mode When a graph is loaded you are in the Study mode When you are creating a new graph or modifying a graph you are in the Modify mode 3 1 1 Begin mode In this mode you can load a graph or create a new one You will find below the description of the items of the menus 11 Files New Create a new graph Prompt for the name of the graph and for its type directed or not directed Then you enter Modify Mode Load Load a graph Show the list of graphs in the default directory You have to choose one Directory Change the default directory Quit Quit Metanet 3 1 2 Study mode In this mode you can load a graph create a new one or work with an already loaded graph With the left button of the mouse you can highlight an arc or a node You will find below the description of the items of the menus Files New Create a new graph Prompt for the name of the graph and for its type directed or not directed Then you enter Modify Mode Load Load a graph Show the list of graphs in the default directory You ha
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