– \u00a0Showing and highlighting\u00a0“significant” changes on\u00a0network evolution. A particular characteristic of interest could be\u00a0the speed with which information flows.<\/p>\n
– Quantifying\u00a0how “close” two networks \u00a0are. Even when the networks have a different different number of nodes and edges, or in the case of spatially embedded networks, different scale.<\/p>\n
As an example, look at the following two networks. Are the structures of\u00a0these two road networks similar?<\/p>\n
![\"Screen](\"https:\/\/luisospina.files.wordpress.com\/2015\/06\/screen-shot-2015-06-15-at-14-56-21.png?resize=625%2C264\")
(Images obtained from the mac Maps app)<\/p><\/div>\n
Or what about the structure of these two other networks?
\n![\"two_geometric\"](\"https:\/\/luisospina.files.wordpress.com\/2015\/06\/two_geometric.png?resize=555%2C260\")
<\/p>\n
One of the difficulties in comparing networks is that there is no clear way to compare networks as complete whole entities. Network comparison methods only compare certain attributes of the network, among these: density of edges, global clustering coefficient, degree distribution, counts of smaller graphs embedded\u00a0in the network and others. Here are some ideas and methods\u00a0that have been used\u00a0as ways to compare networks.<\/p>\n
- \n
- Networks can be compared by their global properties and summary statistics<\/strong>, like network density, degree distribution, transitivity, average shortest path length and others. Usually a statistic combining\u00a0the differences\u00a0of several global properties was used.<\/li>\n
- Another way to compare networks is based on the\u00a0fit of a statistical network model\u00a0<\/strong>(eg.\u00a0\u00a0ERGM<\/a>)\u00a0<\/strong>to each network. Then, the coefficients of the fitted models could be compared. Note that in this case, a good fit of the models would be required<\/em>.<\/li>\n
- Statistics directly built for network comparison via subgraph counts<\/strong>. These statistics\u00a0do not make\u00a0any assumptions of\u00a0the network generation process. For example, Netdis\u00a0and\u00a0GCD\u00a0are\u00a0two network comparison statistics\u00a0that try to measure the structural difference between networks. These network comparison measures are based on\u00a0counts\u00a0of small subgraphs<\/strong> (3-5 nodes), like triangles, 2-stars, 3-stars, squares, cliques and others (see Figure below).\u00a0
![\"subgraph_plot_jpeg\"](\"https:\/\/luisospina.files.wordpress.com\/2015\/06\/subgraph_plot_jpeg.png?resize=470%2C192\")
\u00a0These network comparison statistics create frequency vectors of\u00a0subgraphs and then\u00a0compare these\u00a0frequencies between the networks to obtain an idea of the similarity of the networks relative to their subgraph counts.<\/li>\n- Lastly, another way to indirectly compare<\/strong> networks is via network alignment methods<\/strong>.\u00a0The objective of these methods is to create a “mapping”, f<\/em><\/strong>, from the node set of one network to the node set of another. \u00a0The following Figure shows two networks, light and dark blue. An alignment of the two networks is shown in red.
![\"Screen](\"https:\/\/luisospina.files.wordpress.com\/2015\/06\/screen-shot-2015-06-15-at-21-43-29.png?resize=324%2C198\")
<\/a>One of the objectives of an alignment is to maximise the number of conserved interactions, that is, if (u,v)<\/em> is an edge in the first network and f <\/em>is an\u00a0alignment, then an edge\u00a0(u,v)<\/em> is conserved if (f(u),f(v)<\/em>) is an edge in the second network. It can be noted that the edge demarcated\u00a0<\/em>by the\u00a0green oval is a non-conserved interaction.
\n<\/em>NETAL\u00a0is a\u00a0commonly\u00a0used network alignment method, although there are several, more recent, network alignment methodologies.<\/li>\n<\/ul>\nIn the end, despite the variety of ways to compare networks, saying that two networks are similar, or different, is not that easy, as all methods face their own particular\u00a0challenges, like networks that come from the same model\u00a0but have different node size.<\/p>\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
Nowadays network comparison is becoming increasingly relevant. Why is this? \u00a0Mainly because it is a desirable way to compare complex systems that\u00a0can often be represented as networks. Network comparison aims to account for properties that are generated by the simultaneous\u00a0interaction of all units rather than the properties of each single individual. Here are some cases\u00a0where […]<\/p>\n","protected":false},"author":26,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","wikipediapreview_detectlinks":true,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"ngg_post_thumbnail":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1],"tags":[],"ppma_author":[514],"class_list":["post-2583","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"authors":[{"term_id":514,"user_id":26,"is_guest":0,"slug":"luis","display_name":"Luis Ospina Forero","avatar_url":"https:\/\/secure.gravatar.com\/avatar\/310cef32cd5dac5a383fe35d2e6fa0ed40cb03d0712d2b5a5ef81092db812b3e?s=96&d=mm&r=g","0":null,"1":"","2":"","3":"","4":"","5":"","6":"","7":"","8":""}],"_links":{"self":[{"href":"https:\/\/www.blopig.com\/blog\/wp-json\/wp\/v2\/posts\/2583","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.blopig.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.blopig.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.blopig.com\/blog\/wp-json\/wp\/v2\/users\/26"}],"replies":[{"embeddable":true,"href":"https:\/\/www.blopig.com\/blog\/wp-json\/wp\/v2\/comments?post=2583"}],"version-history":[{"count":3,"href":"https:\/\/www.blopig.com\/blog\/wp-json\/wp\/v2\/posts\/2583\/revisions"}],"predecessor-version":[{"id":2586,"href":"https:\/\/www.blopig.com\/blog\/wp-json\/wp\/v2\/posts\/2583\/revisions\/2586"}],"wp:attachment":[{"href":"https:\/\/www.blopig.com\/blog\/wp-json\/wp\/v2\/media?parent=2583"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.blopig.com\/blog\/wp-json\/wp\/v2\/categories?post=2583"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.blopig.com\/blog\/wp-json\/wp\/v2\/tags?post=2583"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/www.blopig.com\/blog\/wp-json\/wp\/v2\/ppma_author?post=2583"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- Another way to compare networks is based on the\u00a0fit of a statistical network model\u00a0<\/strong>(eg.\u00a0\u00a0ERGM<\/a>)\u00a0<\/strong>to each network. Then, the coefficients of the fitted models could be compared. Note that in this case, a good fit of the models would be required<\/em>.<\/li>\n