It seems that a hierarchical clustering is needed. There might exist some software to handle this.

Dear Prem

Is it directional network? What do edges reflect? Are they weighted?

The answers can help to chose a method. Since the edges in biology network usually tell less than in social network I prefer to use a combination of 2-4 methods, so perhaps here it also will be useful?

Hi Prem

I know two good methods of ranking. The first of them is Pairwise comparison method published by Waldemar Koczkodaj articles "Testing accuracy Pairwise comparison" and "On Axiomatization of Inconsistency Indicators for Pairwise Comparisons"  . The secons is Objective ranking published by Andrzej P. Wierzbicki "Reference Point Approaches and Objective Ranking"

Jan Grzegorek

Hi Prem

It really depends on what you mean by "importance"?!

There are a lot of centrality measures with different algortihms (look up Borgatti & Everet for example) e.g. betweeness centrality or closeness centrality. Might be something you are searching for?!

Cheers, Mathias

Like everything, it all starts from your research question. Are you looking for brokers? Then betweenness is your best measure. Prestige? In-degree. Activity? out-degree. Powerful collaborative partners? eigenvector, alpha or positive bonacich centrality (if  you have some idea of how important neighbours are.  Power within the context of a competitive environment? Negative bonacich centrality.  And so on. All of these depend on your theoretical framework.

Hi Ning Cai , Can you  list out the names of softwares ?

Hi Albert Batushansky , Its a directed network 

Hi Prem, 

I use a method of ranking nodes based on two centrality measures (total degree & Betweenness). You can have a look at one of my papers using this approach below. I use R to compute the ranks. I hope this helps.

Best,

Adina  

Conference Paper The Shifting Discourse of the European Central Bank: Explori...

H i Mathias Mejeh · ,

I'm looking for the  key importance nodes in the network  for information diffusion process . 

Mathias;

A simple way to do it and that can be very useful is utilizares the core-periphery of UCINET function. Only obtaining course to 2 groups but can examine the interaction between both, which can be very interesting.

Alpha centrality is something to examine. Rather than just looking at centrality, Alpha centrality offers you the ability to include an exogenous covariable (wealth? centality values in another network? # of followers on a social media site? etc.). It applies an eigenvector-based measure to both variables that you can weight based on an alpha value (0 = all network; infinity = all exogenous).  Phillip Bonacich has a collection of these sorts of measures that you can explore if you wish:  http://www.leonidzhukov.net/hse/2014/socialnetworks/papers/Bonacich-Centrality.pdf

Which centrality measures did you use?  Why did you not like them?  What are you trying to show?

One measure I like and often use is how many closed triangles does a node belong to? (A is linked to B is linked to C is linked A).  This tends to find those nodes in the dense core as mentioned by Edgar above. Another is diversity -- how many links to how many different groups does a node have?  These tend to be the boundary spanners.

There exist several centrality measures: betweenness, closeness, eigencentrality, katz, google page rank, etc.

A novel approach that take advantage of similarity measures is the contribution centrality (o dissimilarity based centralities) reported in :

http://www.nature.com/articles/srep17095

Best wishes,

Alejandro

http://www.nature.com/articles/srep17095

http://www.nature.com/article-assets/npg/srep/2015/151125/srep17095/extref/srep17095-s1.pdf

Alejandro presents a very interesting new approach to ranking nodes in a network!

One of the key things we must know, before we decide on network measures, is: what is flowing in the network?  And what factors affect that flow? 

The definition of flow depends on the networked systems under study. Moreover, in some cases, where the system has a "channel capacity" or "maximum information rate per link", the flow is capable adapting and taking different paths in a network (avoiding bottle necks). Additionally, you can interpret flow as diffusion or propagation of "information" and this interpretation gives you another set of tools for understanding the meaning of flow in networks. But the fact is that the flow definition/interpretation strongly depends on the system under study.  

Yes, good points Alejandro!

We work with human networks accomplishing tasks and goals in organizations and communities.  Flows in human networks are different than flows in biological networks, pipelines/grids (man-made networks), routers in the Internet, etc.

We also use custom network metrics(based on 20+ years in SNA) with our clients, in addition to the standard centrality et al metrics.

Alejandro, do you have public code implementations of your novel approach? I find it quite interesting and want to test it on a network I am working on. Especially a python implementation would be of great help since I am using networkx python package and its centrality algorithms.

Yes, write me a mail to [email protected]

I wrote a code for Python 2.7 but is easy to translate it to python 3 if you need. 

Regards

Why not attempt an eigenvector approach like PageRank? The algorithm ranks network nodes by their 'importance'. Here's a quick read on PageRank: http://www.cs.princeton.edu/~chazelle/courses/BIB/pagerank.htm