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networks are elegant representations of interactions between individuals in large communities and organizations@xcite .
these networks are constantly changing according to demands , fashions and flow of ideas@xcite .
recently there has been a growing interest in the dynamics of complex networks with a focus on pairwise interactions@xcite .
however , it has often been assumed that the mere existence of a connection in a network implies that transmission of information is complete .
this assumption is associated with the fact that most studies consider static structures derived from all recorded interactions .
often it is less interesting though to know whether two individuals are connected at some point in time and space than it is to quantify the volatility of the link connecting them .
( s.d . ) .
panel b ) and c ) show the temporal variation in the tweet rates of three international brands . in the time signal in panel c ) there is a clear intermittent fluctuation in the overall signal while at the same time there is an underlying periodic variation over days and weeks .
panel b ) shows the corresponding distributions of the tweet rate change @xmath0 measured in hourly intervals . ]    the rapidly growing flux of information through online media permits an unprecedented analysis of human behavior and interactions@xcite .
these interactions can be monitored in real time with a high level of detail via social media such as twitter@xcite .
twitter is a micro - blogging universe where registered users can submit small pieces of information , named `` tweets '' , to an online stream .
the length of a tweet is limited to 140 characters and the content ranges from personal information to massively distributed advertisements or political messages .
twitter has a potentially huge reach and is used by an increasing number of companies and political organizations to disseminate news .    ) . only links with a strength larger than 0.004
are shown .
the network is strongly modular and individual modules have been identified using the spin - glass method@xcite . in panel
b ) , a similar network over major cities in the usa is shown .
links with a strength larger 0.004 are shown . in both panels
pairwise tweet - rates were collected throughout november 2010 and an averaged similarity measures were computed . ]
current tweet rates were measured by submitting repeated search queries to twitter . for each query , up to 1500 of the latest tweets were returned and based on the time interval over which they appeared a rate was calculated .
samples were performed during a 4 month period , november 2010 to february 2011 .
users of twitter have the opportunity to actively follow and re - post tweets , socalled retweets , of other users .
the rate by which a given tweet or user is retweeted provides an instantaneous measure on the community s interest in a given subject .
the distribution @xmath1 of retweet rates @xmath2 of specific tweets and users are shown in fig .  1 .
both distributions have a scale free form on up to five orders of magnitude with an exponent @xmath3 ( s.d . ) , i.e. @xmath4 .
the scale free distribution strongly indicates that the community s interest in a given user or subject is self - organizing@xcite and as a consequence leads to avalanches of retweet rates of all sizes .
avalanches are often associated with an intermittent dynamics where large to extreme events are interrupted by longer periods of quiescent behavior .
this is confirmed by the distribution of the tweet rate change @xmath0 measured in hourly intervals .
the distribution has a clear stretched exponential tail fig .
similar heavy - tail distributions are observed in a number of other systems which show intermittent temporal dynamics .
examples are fully developed turbulence and time series of economical indices @xcite .
the impact of a current subject is influenced by the collective behavior of individuals in social networks .
for instance , the constant stream of information can be used to monitor the real - time popularity of different topics .
moreover , correlations between topics can be measured by analyzing the content of individual tweets , i.e. related topics are likely to appear simultaneously in a tweet as well as in associated retweets .
specifically , we have analyzed correlations within three widely different categories : 1 ) international brands , 2 ) nouns and 3 ) major cities in the usa .
we compiled a list of 100 popular international brands representing top companies in different categories and used a list of the 50 largest cities in the usa .
similarly random samples were taken from a list of 2000 common nouns of the english language .
the similarity of two entities @xmath5 and @xmath6 is defined in terms of the rate @xmath7 by which tweets contain both @xmath5 and @xmath6 .
for example , by considering queries to twitter containing the terms `` google '' and `` microsoft '' , we get @xmath8 per hour and @xmath9 per hour whereas @xmath10 per hour ( january 2011 ) . a normalized symmetric measure of similarity
is naturally defined by @xmath11 in fig .
2 we present networks of international brands and usa major cities created by this measure .
the network of brands is strongly modular with groups of brands representing similar products .
however , some links reveal non - trivial relations between selected brands . for cities
the similarity network provides an alternative map where individual cities only to some extent are grouped according to their geographical location .
the network is dominated by a central module consisting of new york , chicago , atlanta , los angeles and boston .
this is not surprising as these cities are hubs in the american society . in the lower right part
, we observe californian cities in a module that connects naturally to cities like denver and seattle .
we also detect a module of east - coast to mid - western cities connecting to a module of southern cities .
( s.d . ) .
the dashed line is a guide to the eye and corresponds to the computed exponent .
the inset shows distributions of tweet rates of single brands ( purple circles ) , major us cities ( blue triangles ) and english nouns ( green squares ) .
although there is no clear scaling of these distributions we have inserted the same line as in the main panel for comparison . ]    in social media , international brands and to some extent us cities are of global common interest .
fashions spontaneously emerge over a short time span in terms of a collective awareness in the network .
we therefore expect that correlations between current fashions reflect how the awareness percolates on the social network . as a main result ,
we obtain scale free distributions of the pair - wise tweet rates @xmath7 over six orders of magnitude using brands , nouns as well as major cities , see fig .
surprisingly , the distributions are all defined by the same scaling exponent @xmath12 ( s.d . ) .
the distribution of the tweet rates of individual search terms @xmath5 , @xmath13 , does not follow a clear scale invariant distribution ( see inset of fig .  3 ) and
correlations cause the tweet - rate of pairs @xmath7 not to be proportional to the product @xmath14 .
in particular we notice that if the distribution of the rates @xmath15 could be approximated by a scale invariant distribution @xmath16 , we get that the product @xmath17 would follow a distribution @xmath18 the logarithmic correction to scaling does not fit the data of fig .  3
, e.g.  a best fit gives an exponent @xmath19 significantly larger than expected from the distributions of the tweet rates @xmath15 of individual search terms shown in the inset of fig .
we attribute this observation to the interactions between individuals of the social network which generate a common perception of related entities . in other words
, there is an amplification of the frequency by which e.g. certain brands appear together in a tweet . performing a similar analysis using search engines such as google and bing , we achieve different distributions ( see fig .
in contradistinction to social media , the search engines integrate over a long time and include results from widely different media . moreover the search engines include results from web pages which are not restricted in size like the tweets .
the results can be put into further perspective by considering correlations of nouns in a different context . in sentences of novels by e.g. mark twain ( huckleberry finn ) and herman
melville ( moby - dick ) , we recover scale free distributions with significantly larger exponents ( see fig .
the sentences have a typical length comparable to the 140 characters of a tweet .
however , a novel is written by a single author and typically exhibits a more formal structure compared to the text messages created by online interactions between many individuals .
the unique self - organizing behavior of users of social media appears to initiate a cascade dynamics which widens the distributions and lowers the scaling exponent relative to that of novels .
a deeper understanding of this effect calls for an uncovering of mechanisms behind human communication on online media .
social media have become vital channels for advertising as well as disseminating news and political opinions , therefore this understanding will have significant potential not only in several branches of science but also for commercial purposes .
the fact that the complex communication patterns appear to be universal indicates that the information flow on social media is a reflection of basic human behaviour .
( huckleberry finn ) and @xmath20(s.d . )
( moby - dick ) .
inset : probability density function of the frequencies by which individual nouns appear in the same sentences .
, title="fig : " ] ( s.d . )
( huckleberry finn ) and @xmath20(s.d . )
( moby - dick ) .
inset : probability density function of the frequencies by which individual nouns appear in the same sentences .
, title="fig : " ]
suggestions and comments by kim sneppen and namiko mitarai are gratefully acknowledged .
this study was supported by the danish national research foundation through the center for models of life .
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social media have become essential conduits in the worldwide exchange of ideas , opinions and consumer marketing . 
 complex networks are important tools for analyzing the information flow in many aspects of nature and human society . here 
 , we introduce a method based on networks and social media to gauge how ideas , opinions and new trends impact society . 
 we show that correlations between different international brands , nouns or us major cities follow a universal scale free distribution . 
 the correlations indicate a self - organizing dynamics in large social organizations where the exchange of information between individuals is highly volatile . 
 our method provides new fundamental insight on the propagation of opinions and the emergence of trends in online communities .