Information Propagation on Twitter
Eldar Sadikov Maria Montserrat Medina Martinez Stanford University Stanford University [email protected] [email protected]
Goal ABSTRACT A and may not receive B’s tweets. These connections nat- We analyze URL and tag propagation on Twitter social net- urally• Study form information a directed social propagation network where on nodesTwitter are from the work with 54 million nodes and 1.5 billion edges, one of the usersthe of thenetwork service standpoint and edges represent the subscriptions. largest social networks studied in academia. We specifically focus on the interplay of external and network influences. Secretary of state Clinton announces 2012 Int’l AIDS conference We attribute propagation to the network whenever a user to be held in U.S.: http://bit.ly/8Bc #WorldsAIDSDay mentions a tag or URL after one of its neighbors has pre- • Given:Figure 1: An example of a tweet viously mentioned it, and to external influence otherwise. Tweets, as shown in Figure 1, often contain URLs and We develop a new metric to measure external influence and – The social network tags. Tags are tokens prefixed with a #, e.g. “WorldsAIDS- an efficient algorithm to calculate it. The insight we obtain – Sequence of nodes that mentioned a hashtag or Day”in Figure 1, and often used to indicate the tweet’s topic from the external influence metric paired with the analysis URL in chronological order or event. On the other hand, URLs are typically HTTP links of cascade dynamics of the network influence, not only val- to• newsStudy articles, topology pictures, and or characteristics videos. of infected idates some of the previously observed phenomena in other Innodes this paper, in the we studygraph the propagation of URLs and tags social networks but also provides new insight into the inter- over the Twitter social network. Specifically, we look at the play of network and external influences over the lifetime of users (i.e. nodes in the network) that mention a particular memes in the network. URL or tag in chronological order, their distribution over the network, and the presence/absence of edges between them. Categories and Subject Descriptors We will generally refer to such chronological distribution as H.2.8 [Database Management]: Database applications— information propagation, where information, in our context, Data mining will refer to the URLs and tags. There are a number of factors that make Twitter inter- esting for studying information propagation and make our General Terms work different from the previous work in the area. First of Experimentation, Measurement, Algorithms all, Twitter, unlike much of the previously studied media such as news feeds, blogs, emails, has an explicit social (i.e. Keywords subscription) network. Our work is one of the first ones to look at information propagation on a real social network Social networks, information propagation which is, on top of all, one of the largest ones known to date. Second of all, because information on Twitter often spreads 1. INTRODUCTION in the form of tags and URLs, there is no burden of data Twitter is a social networking and micro-blogging service cleaning and thus no potential bias in results. Thirdly, Twit- which has become popular over the last couple of years. ter URLs and tags, in themselves, are interesting to study Twitter users send and read messages known as tweets. Tweets, as people often now rely on them to find trends and news as shown in Figure 1, are text-based posts up to 140 char- on the web. acters long and are delivered to the author’s subscribers, While Twitter users can discover information directly from known as followers. Such subscriptions form directed not al- the network, i.e. by reading the tweets of the users they fol- ways symmetric connections, where user A may follow user low, they can equally discover information from outside of B and, hence, receive A’s tweets, but user B may not follow the network, e.g. from TV, newspapers, online news aggre- gators (e.g., Google News), etc. In this work, we attempt to understand how to differentiate between the two cases and propose new metrics to quantitatively analyze them. To our knowledge, this is one of the first attempts to study Permission to make digital or hard copies of all or part of this work for the contribution of external sources to information spread personal or classroom use is granted without fee provided that copies are in social networks. Moreover, most of the work up to date not made or distributed for profit or commercial advantage and that copies has focused on propagation directly via the network, i.e., in bear this notice and the full citation on the first page. To copy otherwise, to our setting, the case when users find information directly republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. from the people they follow. However, even to this respect, Copyright 200X ACM X-XXXXX-XX-X/XX/XX ...$10.00. our findings not just confirm the already observed phenom-
1 ena, but also unveil new interesting dynamics. Last but not disease propagation model [1], where once infected, a node least, the findings we report in this paper have applications cannot be reinfected (all mentions of some URL or tag x in news and trend detection and tracking. after the first mention are ignored). In summary, our contributions are as follows: Cascades: • Basic analysis of Twitter social network properties (Sec- Definition 7. For a given infection hx, hv1, v2, . . . , vnii, tion 3) we define its infection graph at step k, 1 ≤ k ≤ n, as a • Metric to measure the contribution of external sources subgraph Ck(Vk,Ek) of G(V,E), where Vk = ∪1≤i≤kvi and to information propagation in a social network: 1) its there is an edge (vi, vj ) ∈ Ek iff (vi, vj ) ∈ E and i < j. formal definition, 2) efficient algorithm to compute it, Definition 8. In a given infection graph Ck(Vk,Ek), we 3) its evaluation on real data and 4) comparison of its refer to its connected components as cascades. behavior on real data to two simple synthetic informa- tion propagation models (Section 4) Definition 9. A cascade is said to be non-trivial if its • Comprehensive analysis of the network contribution to size is greater than 1. the spread of URLs/tags on Twitter (Section 5) Definition 10. A node vk is said to be cascaded if for a given infection hx, hv , v , . . . , v ii and its graph C (V ,E ), 2. PRELIMINARIES 1 2 n n n n vk is in a non-trivial cascade. We begin by introducing our terminology and notation. Definition 11. For infection hx, hv1, v2, . . . , vnii and its Network: Given subscription (i.e. follow) relationships 0 between Twitter users, we define the Twitter network as graph Ck+1(Vk+1,Ek+1), 1 ≤ (k + 1) ≤ n, let V be the set a directed graph G = (V,E), where each node in V is a of incoming neighbors of vk+1. Node vk+1 is said to merge cascades if the nodes in V 0 belong to more than one cascade Twitter user. For any two users v1 ∈ V, v2 ∈ V there is an in the graph Ck(Vk,Ek) at step k of the same infection. edge (v1, v2) ∈ E if and only if v2 follows v1. In other words, we introduce an edge from v1 to v2 as long as v2 subscribes to tweets of v1, and, hence, information in the form of URLs 3. DATA SET or tags posted by v is observed by (i.e. flows to) v . 1 2 Network: We have been continuously monitoring a sample
Definition 1. For any two nodes vi ∈ V and vj ∈ V , of all publicly available tweets over the last six month and, the distance d(vi, vj ) from vi to vj is defined as the shortest from each observed user ID among the collected tweets, we directed path in the network from vi to vj . If such path does explored the Twitter network structure in a breadth-first- not exist, d(vi, vj ) = ∞. search manner. We collected this way follow relationships (i.e. IDs of people a user follows) for almost 54,310,622 users Stream: which is 99.9% of all user IDs known to us. The graph we have obtained has 1,491,979,651 edges with average number Definition 2. Tweet is a triple hv, m, ti, where v ∈ V of followees (in-degree of a node in the network, per our is the user who posted the tweet, m is the text of the tweet definition) per user at 27.47. (message), and t is the time when the tweet was posted. Here we provide some other basic stats on the collected network. Definition 3. Stream is a sequence of tweets hhv1, m1, t1i, hv2, m2, t2i,...i, where any tweet hvi, mi, tii precedes another • Figure 2 shows the out-degree distribution of the net- tweet hvj , mj , tj i iff ti ≤ tj . work plotted on the log-log scale, i.e. the distribution of the number of followers per user. One can observe For simplicity, we will assume that we have access to only that the distribution follows the power law. The power one stream. This stream may either contain all publicly law exponent is 1.95, estimated by the complementary available tweets or a sample of all the tweets. cumulative distribution function (CCDF) method, and Definition 4. For a given URL or tag x, user v men- 1.84, as estimated by the maximum likelihood estimate (MLE) method. tions x if there is a tweet hv, mi, tii in the stream, such that x is contained within mi. 100 100
-1 -1 5. For a given URL or tag x, the first men- 10 10 Definition 10-2 10-2 tion of x by user v is the first tweet hv, mi, tii in the stream, 10-3 10-3
10-4 10-4 such that x is contained within mi. If v does not mention p(x) p(x) x, the first mention of x by v does not exist. 10-5 10-5 10-6 10-6
-7 -7 6. An infection is a pair of some tag or URL 10 10 Definition 10-8 10-8 100 101 102 103 104 105 106 107 100 101 102 103 104 105 106 x and a sequence of nodes hv1, v2, . . . , vni (infection sequence) Vertex degree Vertex degree of some length n, such that a node v belongs to the sequence iff it mentions x and for any i, j, 1 ≤ i < j ≤ n, the first Figure 2: Degree distribution of Twitter network: mention of x by vi is before the first mention of x by vj . a) outgoing (followers) b) incoming (followees).
Note here that according to this definition of infection, a • Figure 2 shows the in-degree distribution of the net- node can appear in the infection sequence only once. In work plotted on the log-log scale, i.e. the distribution other words, we use Susceptible-Infected-Recovered (SIR) of the number of followees per user. Although there are
2 106 100 Outgoing Incoming Stream: We have collected 33% sample of all publicly 105 available tweets from mid June through the end of October 104 of this year with up to 5 million tweets per day. To simplify 103 10-1 processing, we focused only on the 10-day period from Au-
102
Clustering coefficient gust 1 until August 10. From this 10-day period with the Number of Components 101 total of 45 million tweets, we extracted all of the URL and
100 10-2 100 101 102 103 104 105 106 107 108 100 101 102 103 tag mentions. We have found 315,000 distinct tags and 9.5 Component Size k (Degree) million distinct URLs after translating short URLs to long Figure 3: a) Weakly connected components size dis- URLs. We proceeded by picking a sample of 20 most popu- tribution b) Clustering Coefficient as a function of lar URLs and 15 most popular tags with a distinct spike in vertex degree. mentions in the middle of Aug. 1 - Aug. 10 and no or little activity in the beginning and end of this time interval. All a few spikes, overall, the distribution also follows the of the analysis in what follows is based on these 20 URLs power law. The power law exponent is 2.13, estimated and 15 tags with 1000 mentions per each, on average. by the CCDF method, and 1.90, as estimated by the Synthetic Models: Our main objective is to study the MLE method. The spikes can be explained by the ex- interplay between the external and network influences in in- isting follow limits, enforced by Twitter. Specifically, formation propagation on Twitter. Hence, to put our results one cannot currently follow more than 2000 people un- in perspective, we would like to have some basis for compar- less she is followed by at least 2000 people. Hence, we ison. For this, we developed two primitive models of infor- observe in Figure 2 a spike at the vertex degree of 2000. mation propagation that represent two extremes: one where The subsequent spikes may also be due to the follow only external sources contribute to information propagation limits: beyond 2000 friends, Twitter enforces follow and one where all the contribution is due to the network. limits proportionally to the current number of follow- ers. The small spikes before 2000 could be possibly • We will call the first one Random , where we produce due to other similar constraints enforced by Twitter. an infection, by picking at each step a node uniformly at random from the network, as long as it is different • Figure 3 shows the distribution of weakly connected from the previously picked ones. components by size. As observed with many other • We will call the second one RC (for“Random Cascade”), social networks, there is a giant connected compo- where we pick the first node uniformly at random from nent that includes 99.9995% of the graph. The second the network, and generate the subsequent ones by pick- largest component has only 43 nodes. ing at random a neighbor of already infected nodes (at step 2, there is one such node, at step 3, there are two • Although the clustering coefficient was originally de- such nodes, etc.), again as long as it is different from fined for undirected graphs [4], we extend its definition the previously picked nodes. to directed graph as follows. For a vertex vi, we define its clustering coefficient to be For each of these two models, we generate 10 infections with 1200 nodes each and, when reporting results, use the average P 1{(vj , vk) ∈ E} vj ∈Ni,vk∈Ni,vj 6=vk of these 10 generated infections. Ci = |Ni||Ni − 1| 4. EXTERNAL INFLUENCE If Ni is the set of outgoing neighbors, i.e. followers, of vi, then Ci is defined as the outgoing clustering coeffi- 4.1 External Influence Metric cient of v . Equivalently, if N is the set of incoming i i If there is a major event that happens externally to the neighbors, i.e. followees of v , then C is defined as the i i network, e.g. death of Michael Jackson or Barack Obama incoming clustering coefficient of v . i winning the Noble prize, memes (URLs and tags) about it Now, using these definitions, in Figure 3 we plot incom- may spread through the network quite sporadically and in- ing and outgoing clustering coefficients as a function dependently of the edges between the nodes that mention of vertex in-degree and out-degree, respectively, up to them. For example, consider a sample network in Figure 4. 1000. The average incoming clustering coefficient is Suppose node o mentions some meme (i.e. gets infected), 0.12 and the average outgoing clustering coefficient is followed by a, and finally followed by i. Clearly, a could 0.05. The incoming coefficient curve has a number of not have gotten this meme from o, as there is no directed “dips” at the same exact points that incoming degree path between them. On the other hand, assuming that in- distribution has spikes. Granted that the spikes in in- formation cannot flow via more than one edge at a time, i degree distribution are due to the follow limits, it is could not have gotten this meme from a or o either. The natural that as people force their number of followees shortest path to a from the “infected” nodes is {i, h, g, d, a} to reach the limit, fewer of these people will follow consisting of 4 edges. each other among themselves. On the other hand, ob- In general, whenever a newly infected node x has no edge serve that the outgoing clustering coefficient has a sine from any of the currently infected nodes, we can assume x wave shape in the beginning. We believe this is due to could not have possibly gotten infected through the network. spam on Twitter: users with low out-degree are typ- Now suppose that the social network distance between any ically users with low activity or new users, thus they two nodes is proportional to the social distance between two have few friends who follow them and the percentage people in real life. Then, intuitively, some major event dif- of spam users that follow them is higher than average. fused by many external sources is likely to spread over larger
3 e Algorithm 1 multiSourceBFS(S,t,G)
b f m queue ← priorityQueue.new() o 2 a j 1 for s ∈ S do c g n queue.InsertWithPriority(s,1)
d k end for h while !queue.isEmpty() do l 3 i d ← queue.getPriority() // current best priority vi ← queue.getNext() Figure 4: External influence example for all vj , s.t. (vi, vj ) ∈ E do distances within the social network than some minor event if vj = t then (event local to some community). Accordingly, to measure return d + 1 the influence of external sources on meme propagation we else would like to have some notion of network distance traversed queue.InsertWithPriority(vj ,d + 1) by the infection to reach all currently infected nodes. end if For any given infection hx, hv1, v2, . . . , vnii, as defined in end for Section 2, to measure the contribution of external sources end while to its propagation by each step i, we develop the following 600 250 metric, intuitively equal to the minimum distance traversed Tags Tags URLs URLs 500 Random by the infection in the network: Random Cascade 200 400 i 150
X ! 300 ! θi = min {d(vt, vk), dmax + }, where 100 1≤k
4 103 102 Tag Tag 5. NETWORK INFLUENCE URL URL Random 102 In this section, we study how the network contributes to Random Cascade 101 the propagation of tags and URLs on Twitter. In other 101 100 words, we look at how much of meme popularity can be at- 100 Node count Cascade count tributed to users copying the meme from the users they fol- 10-1 10-1 low. Using the terminology introduced in Section 2, we look 10-2 10-2 at 1) how infection graphs and, specifically, cascades (their 100 101 102 103 104 100 101 102 Infections Produced Cascade depth connected components) look like for URLs and tags; 2) how they evolve as more nodes are infected; 3) what structural Figure 7: a) Number of infected neighbors vs. num- properties of edges and nodes can be indicative of cascade ber of such nodes b) Cascade depth vs. number of formation. such cascades.
100 5.1 Structure of Infection Graphs Tag URL
For each URL and tag, we have constructed its infection 10 graph and looked at all of the cascades. On average, 55% of nodes are cascaded for URLs and 45% of nodes are cascaded 1 for tags. As observed in [2] with recommendation networks
% of infected nodes 0.1 and in [3] in blog graphs, we have found that infection graphs frequently have a large connected component. On average, 0.01 1 10 100 it contains 86% of all cascaded nodes for URLs and 73% of Cascade Size as a % of the largest Cascade all cascaded nodes for tags. Figure 8: Cascade size vs. number of % of nodes in Next, we attempt to understand how the typical cascades such cascades (largest cascade excluded) look like for URLs and tags. If cascades are star-shaped, a few central nodes may be responsible for meme propagation on the network, whereas if cascades are chain-like or tree- What we have found is that some of the tags do not have a shaped, nodes participating in the infection contribute to prominent largest cascade, but rather have many medium- the cascades more evenly. sized cascades. Moreover, even when there is a prominent largest cascade, there are still quite a few medium-size cas-
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18027950 14354011 16007332 7376382 cades. As a result, there is a lot of weight under the left 40092662 16282177 16414414 46826084 2521391 21268412 15581619 33001102 54817632 33762255 30233886 19563907 16004574 17770553 15157595 15279698 side of the Tags curve, whereas cascade size distribution for 792537 15850970 21767828 930881 22499388 18480781 15670461 12687952 15875472 15256532 17873060 14861224 843031 14396862 12236142 14275605 16812760 19865122 3568351 45773 60654757 19739208 19803185 20649423 14899361 18064229 29925181 21031608 22477825 15967393 14511820 58710375 14670841 16147974 15161199 14059222 6837002 6837852 URLs, as expected, follows the power law with the second 5758422 74673 19303336 16999739 16581661 12956852 10883722 14983646 14513407 17010143 15171141 12513472 17374514 17121324 27124617 15356119 15036089 5911382 16311307 8067362 12381672 14870618 8609952 14871157 9320582 15936344 23338037 14938378 18208855 16746001 14655634 22427399 19573754 38594061 19504723 22634420 17413657 14186995 16480818 34142998 15841388 18684522 14577069 5671372 19126790 largest cascade being only 10% of the largest one. 53575423 17388181 58625172 12503502 10952772 26725463 17778232 16151404
5259391 28833993 5.2 How Cascades Evolve with Time Figure 6: An example of a cascade Having observed that tags exhibit more external influence Figure 6 illustrates the largest cascade for one of the memes and tend to have larger cascades, we would like to under- we analyzed. One can observe that overall it has a tree struc- stand the cascade growth dynamics over time. First, we ture with a surprisingly high depth, given the low diameter would like to verify that the higher external influence ob- of social networks. Furthermore, there are a few nodes with served for tags is due to the emersion of disjoint larger cas- high out-degree that might have originated as star-shaped cades. Second, we would like to confirm that the growth cascades before merging into the main one. of the largest cascade is generally due to the absorption of To understand the frequency of high out-degree nodes, we smaller cascades, as suggested in [2]. plot in Figure 7 (a) the number of nodes vs. the number In Figure 9, we plot the number of cascaded nodes, size of of infections they produced averaged across all URLs and the largest cascade, and the number merged cascades within tags. The overall distribution follows the power law with a the largest one as a function of the % of infected nodes for heavy tail. Clearly, the nodes in the tail contribute to the both URLs and tags. Observe the steep slope of both cas- propagation of memes more heavily than the other nodes. caded nodes and the largest cascade curves in the beginning Finally, observe how the RC closely mimics the dynamics of of a meme lifetime. This indicates that the cascading be- URLs and Tags. This is not surprising because the number havior starts strongly and quickly forms the largest cascade. of infected neighbors in RC is directly proportional to the The same can be confirmed by the initial dip in the number degree of the node and inversely proportional to the time of of merged cascades within the largest component. infection, which will naturally generate a power law distri- The second observation we make is that the growth of the bution.To further understand the shape of cascades, we look at largest cascade is much more rapid for tags than for URLs. their average depth. Figure 7 (b) shows the depth of a cas- This can be seen better in Figure 10 (a), which shows the cade vs. the number of such cascades. Except for the bump growth of the largest cascade as function of the % of infected at the end, the distribution again follows the power law. The nodes. Furthermore, whereas the largest cascade has more bump is due to the largest cascade for each meme which, as or less steady growth for URLs, its growth actually slows we have observed in Figure 6, is generally quite deep. down over time for tags. Although there is almost always a prominent largest cas- Now that we know the general tendency in the growth of cade, we have looked into how big are the rest of the cas- the largest cascade, we look into how the growth is achieved cades. Figure 8 shows the cascade size expressed as a % of over time. Figure 10 (b) shows the number of merged cas- the largest cascade vs. the number of nodes in such cascades. cades (as a % of the largest cascade size) within the largest We specifically exclude the largest cascade from the figure. one over time (as more nodes are infected). We note the
5 60 60 0.009 0.012 Tag 0.008 URL 50 50 Random Cascade 0.01 0.007 40 40 0.006 0.008 Cascaded Nodes Cascaded Nodes 0.005 Tags 30 Largest Cascade 30 Largest Cascade 0.006 Urls Number of Roots Number of Roots 0.004 Random Cascade 20 20 0.003 0.004 Probability of Infection
Probability of Infections 0.002 10 10 0.002 0.001 % count relative to infected nodes % count relative to infected nodes 0 0 0 0 0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 90 100 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 % of infected Nodes % of infected Nodes % of Infected Friends % of Mutual Friends
Figure 9: Cascade dynamics over time a) URLs b) Figure 11: a) Adoption Curve b) Probability of Tags adoption vs. % of mutual friends or weak links tend to form cascades. Figure 11 (b) shows 50 102
45 the probability of adoption/infection vs. the % of mutual 1 40 10 neighbors. Specifically, if x is infected and y is its outgoing
35 neighbor, we calculate the percentage of common outgoing 100 30 edges for x and y. We used the same filtering criteria to 25 10-1 ensure that our results are statistically significant. As seen 20 Tag Tag URL
% of nodes in the largest cascade from the figure, for tags, the more mutual neighbors y has URL -2 Random Cascade
15 # of merged cascades as a % largest 10 0 10 20 30 40 50 60 70 80 90 100 100 101 102 103 104 with x, the more likely y is to get infected, i.e. strong links % of infected nodes Number of Infected Nodes are more likely to propagate tags. On the other hand, for Figure 10: a) Growth of largest cascade over time URLs the results are again inconclusive. The curve behaves b) Number of merged cascades within the largest in the same manner as RC , which suggests that strong links cascade over time are just as likely to propagate as weak links. Intuitively, with tags, one is more likely to agree with somebody who is a close initial decline in the % of merged cascades indicating that friend (possibly with many shared interests), whereas, with the initial growth of the largest cascade is mostly internal. URLs, we are just as likely to share information obtained In the middle, however, for both URLs and Tags we observe from close friends as the one from distant friends. the ratio staying quite steady suggesting that the largest cas- cade starts absorbing many smaller ones. Finally, at the end of the infection lifetime, we observe two different trends for 6. CONCLUSION URLs and tags. Tags have multiple abrupt drops, whereas In this paper we looked at tag and URL propagation on URLs have a few sharp spikes. This suggests that the largest Twitter social network. After developing a new metric to cascade for tags either exhibits a lot of internal growth or measure the external influence, we have found that external more likely (based on the previous results) absorbs many sources have a significant contribution to URL and tag prop- larger cascades. In contrast, the largest cascade for URLs agation. As the tag becomes popular on Twitter, it travels grows by absorbing many more small ones. to more distant parts of the network and forms relatively large cascades that over time start merging into the main 5.3 Which nodes tend to cascade giant cascade. On the other hand, URLs travel shorter dis- In this section, we look into which nodes are more likely tances in the network and tend to spread mostly by forming to cascade. If one was to do a prediction on whether and many small cascades that merge into the giant cascade. Fi- how a meme is going to propagate through the network, it nally, we found the that the probability of adoption of a tag is important to understand what nodes tend to cascade and is directly related to the number of neighbors who already thus which parts of the network the infection is likely to adopted and the strength of ties with them. On the other reach. hand, for URLs, such tendencies do not hold. Among the First, we plot the adoption curve in Figure 11 (a), i.e. future directions we would like to validate the dynamics we the probability of adoption/infection vs. the % of incom- have observed on a larger set of tags and URLs and try to ing infected neighbors. Here, we exclude the data points develop a model that would predict future propagation of with few number of occurrences: for a given % of infected URLs or tags at an early stage. friends, if the number of such observed cases was less than 4000 we ignored it. With generally low probability of adop- 7. REFERENCES tion, using too few cases may yield statistically insignificant [1] R. Anderson and R. May. Infectious Diseases of conclusions. After such filtering, we can observe how the Humans: Dynamics and Controls. Oxford University probability of adoption for tags generally increases with the Press, 2002. % of infected neighbors. On the other hand, for URLs even [2] J. Leskovec, L. A. Adamic, and B. A. Huberman. The though there is a general upward tendency, the results are dynamics of viral marketing. ACM Trans. Web, 1(1), inconclusive: the general trend is similar to the random be- 2007. havior of RC . Our intuition for why the chances of infection increase with the number of infected neighbors for tags and [3] J. Leskovec, M. Mcglohon, C. Faloutsos, N. Glance, and not for URLs is that URLs are mostly used to share infor- M. Hurst. Cascading behavior in large blog graphs. In mation, whereas tags are often used as a sign of solidarity. In SDM, 2007. Peer pressure will only increase the chances of agreement for [4] D. J. Watts and S. H. Strogatz. Collective dynamics of tags, whereas for URLs, redundancy in information will not small-world networks. Nature, 393(6684):440–442, June increase the chances of adoption. 1998. The next question we try to answer is whether strong links
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