hig.rar_Free!

%% B-A Scale-Free Network Generation and Visualization % *By Mathew Neil George* %% Description and Cautions % The *SFNG* m-file is used to simulate the B-A algorithm and returns scale-free % networks of given node sizes. Understanding the B-A algorithm is key % to using this code to its fullest. Due to Matlab resource limitations, it may not be % possible to generate networks much larger than 15000 nodes, and increasing the % *mlinks* variable increases processing time severely. This code was % developed so that one could generate a network of small size, and then % use that network as a seed to build a greater sized network, continuing % this process until the actual desired network size is reached. This is for % processor and time management purposes. However, realize that the initial % seed does not have to have scale-free properties, while the later seeds % may happen to have these properties. Therefore, it is prudent not to make the % initial seed size much larger than a few nodes (most commonly 5 % interconnected nodes). In addition, the *mlinks* should be kept constant % throughout the creation of the scale-free network. % % The *PLplot* m-file takes a scale-free network in adjacency matrix format % and draws a best fit line to the frequency of degrees distribution of the % nodes. Degree is the number of links that connect to and from a single node % For scale-free networks, the frequency of degrees distribution forms a % power-law curve, with an exponent usually between -2 and -3. This code is % designed to allow only non-zero frequencies to be graphed in log-log format. % The function returns the equation of the power-law fit in a cfit variable. % % The *CNet* m-file function creats a network graph using the *gplot* % function with circular coordinates. It allows for a simple, yet % intuitive, visualization of a given network. %% Parameters % *SFNG* % % * *Nodes* is the desired network size, including the seed network size % (i.e. Nodes minus seed network size equals the number of nodes to be % added). % % * *mlinks* controls the number of links a new node can make to the existing % network nodes. % % * *seed* is the original network to which the B-A algorithm links % additional nodes with a specific preferential attachment procedure. % This undirected adjacency matrix can be created manually, or one could % use the *Adjacency Matrix GUI*. Each node must have at least one link. % The *seed* variable can be replaced with a developed scale-free network % to generate a larger one. Make sure the new *Nodes* variable is greater % than the size of the *seed* network. % % *PLplot* % % * *Net* is the input network which is to be graphed. % % *CNet* % % * *Net* is the input network which is to be graphed. % % Note that variables *Nodes*, *mlinks*, and *size* must be whole numbers and % variables *seed* and *Net* must be undirected adjacency matrices. The % diagonol elements of any adjacency matrix used with these functions must % all be zero. %% Sample Output % Here is a small example to demonstrate how to use the code. This code % creates a seed network of 5 nodes, generates a scale-free network of 300 nodes from % the seed network, and then performs the two graphing procedures. seed =[0 1 0 0 1;1 0 0 1 0;0 0 0 1 0;0 1 1 0 0;1 0 0 0 0] Net = SFNG(300, 1, seed); PL_Equation = PLplot(Net) CNet(Net) %% References % One explanation of the B-A Algorithm can be found on this PDF website % http://arxiv.org/PS_cache/cond-mat/pdf/0107/0107420.pdf % % Undirected Adjecency Matrices are defined on Wikipedia.org % http://en.wikipedia.org/wiki/Adjacency_matrix % % The *Adjacency Matrix GUI* file by Steve Chuang can be found on the Matlab File Exchange % http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=6937&objectType=file %% Acknowledgements % Special thanks to Mark Ballerini with the Massapequa High School Science % Research Program and Zoltan Dezso at the University of Notre Dame for % their invaluable help in researching network theory as well as to my % family for providing motivation and encouragement in pursuing science.