matlab - Determine whether a network (graph) is connected based on its matrix -


how can determine given m x n matrix desribing two-mode network whether connected or not?

of course once can create data structure finding out – there mathematical solution?

i found out n x n matrices (one-mode network) easy: solution be: m * m , looking @ diagonal in resulting matrix. if there 0 on diagonal not connected. isn't true?

what suggestion both problems?

it not simple one-mode networks, you're close.

the network matrix m tells node connected other node in 1 step. m * m tells node connected other node in exactly two steps, m ^ 3 whether in exactly three steps, , on. "exactly" important, because if nodes not connected (zero diagonal elements), m * m not obtain two-step connectivity, loses one-step connectivity.

the products (powers) therefore more useful if nodes connected themselves:

a = (m + eye(size(m)) > 0)

this step converts weighted matrix pure adjacency matrix. now

(a ^ > 0)

gives information whether 2 nodes connected in i steps or less. in network n = size(m, 1) nodes, distance between 2 nodes can @ n - 1 steps. therefore

c = (a ^ (n - 1) > 0)

gives information whether 2 nodes connected at all. whole network connected if there no pairs of unconnected nodes, i.e. if

connected = (sum(c(:)) == n ^ 2)

i'm not sure how 1 define connectedness in two-mode network. simple approach disregard difference between 2 types of nodes, , consider them part of one-mode network. if m original two-mode network matrix of size [m, n] = size(m), 

m = [zeros(m, m) , m ; m' ; zeros(n, n)];

converts matrix describing corresponding one-mode network of size (m+n)x(m+n).

these matrix powers not tell whether whole network connected, can used find connected sub-networks (network clusters) if not. since behavior of powers of matrix closely connected spectral decomposition (a.k.a. eigendecomposition), idea leads approach of spectral clustering. application weighted synchronization networks, see e.g. arxiv:0706.3375.


Comments

Post a Comment

Popular posts from this blog

apache - Remove .php and add trailing slash in url using htaccess not loading css -

i have add following code htaccess file removing .php extension , add trailing slash urls. worked fine reduced page loading speed , css code not loading @ all. pages ugly. please help rewriteengine on rewritebase / ## hide .php extension snippet # externally redirect /dir/foo.php /dir/foo rewritecond %{the_request} ^[a-z]{3,}\s([^.]+)\.php [nc] rewriterule ^ %1/ [r,l] # add trailing slash rewritecond %{request_filename} !-f rewritecond %{request_uri} !/$ rewriterule . %{request_uri}/ [l,r=301] # internally forward /dir/foo /dir/foo.php rewritecond %{request_filename} !-d rewritecond %{request_filename}.php -f rewriterule ^(.*?)/?$ $1.php [l] we can rewrite urls using .htaccess files. before writing in .htaccess files need verify kind of server using. can check server adding a <?php phpinfo(); ?> in php page. ensure mod_rewrite module enabled in apache server. can identified checking phpinfo included page. common methods used url rewriting follows ...
Read more

javascript - jQuery show full size image on click -

pretty self explanatory not workking . i want display full image when user click on image... yes know there tons of plugins but i want keep simple. any idea ? css : .full { display: none; width: 500px; height: 500px; margin-left: 100px; margin-top: -300px; position: fixed; background-color: #f00; z-index: 6; } .thumbnail { width: 50px; height: 50px; } html: <img class="thumbnail" src="http://4.bp.blogspot.com/-uhbdp2esxng/txneptvi92i/aaaaaaaaaky/upfqis7zto0/s1600/rihanna-wallpaper.jpg"> jquery: $(document).ready(function() { $('.thumbnail').on('click', function() { var img = $('<img />',{src:this.src,'class':'full'}); $('.full').html(img).show(); console.log('done!'); }); }); try looking how jquery works. $(document).ready(function() { $('.thumbnail').on('click', function(...
Read more