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61
Analysis of Topological Characteristics of Huge Online Social Networking Services.
- In Proc. of ACM WWW,
, 2007
"... ABSTRACT Social networking services are a fast-growing business in the Internet. However, it is unknown if online relationships and their growth patterns are the same as in real-life social networks. In this paper, we compare the structures of three online social networking services: Cyworld, MySpa ..."
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Cited by 260 (6 self)
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ABSTRACT Social networking services are a fast-growing business in the Internet. However, it is unknown if online relationships and their growth patterns are the same as in real-life social networks. In this paper, we compare the structures of three online social networking services: Cyworld, MySpace, and orkut, each with more than 10 million users, respectively. We have access to complete data of Cyworld's ilchon (friend) relationships and analyze its degree distribution, clustering property, degree correlation, and evolution over time. We also use Cyworld data to evaluate the validity of snowball sampling method, which we use to crawl and obtain partial network topologies of MySpace and orkut. Cyworld, the oldest of the three, demonstrates a changing scaling behavior over time in degree distribution. The latest Cyworld data's degree distribution exhibits a multi-scaling behavior, while those of MySpace and orkut have simple scaling behaviors with different exponents. Very interestingly, each of the two exponents corresponds to the different segments in Cyworld's degree distribution. Certain online social networking services encourage online activities that cannot be easily copied in real life; we show that they deviate from close-knit online social networks which show a similar degree correlation pattern to real-life social networks.
Quantifying social group evolution
- Nature
, 2007
"... The rich set of interactions between individuals in the society [1,2,3,4,5,6,7] results in complex community structure, capturing highly connected circles of friends, families, or professional cliques in a social network [3,7,8,9,10]. Thanks to frequent changes in the activity and communication patt ..."
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Cited by 126 (3 self)
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The rich set of interactions between individuals in the society [1,2,3,4,5,6,7] results in complex community structure, capturing highly connected circles of friends, families, or professional cliques in a social network [3,7,8,9,10]. Thanks to frequent changes in the activity and communication patterns of individuals, the associated social and communication network is subject to constant evolution [7,11,12,13,14,15,16]. Our knowledge of the mechanisms governing the underlying community dynamics is limited, but is essential for a deeper understanding of the development and self-optimisation of the society as a whole [17,18,19,20,21,22]. We have developed a new algorithm based on clique percolation [23,24], that allows, for the first time, to investigate the time dependence of overlapping communities on a large scale and as such, to uncover basic relationships characterising community evolution. Our focus is on networks capturing the collaboration between scientists and the calls between mobile phone users. We find that large groups persist longer if they are capable of dynamically altering their membership, suggesting that an ability to change the composition results in better adaptability. The behaviour of small groups displays the opposite tendency, the condition
Statistical analysis of the social network and discussion threads in slashdot
- IN: WWW, ACM
, 2008
"... We analyze the social network emerging from the user comment activity on the website Slashdot. The network presents common features of traditional social networks such as a giant component, small average path length and high clustering, but differs from them showing moderate reciprocity and neutral ..."
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Cited by 86 (12 self)
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We analyze the social network emerging from the user comment activity on the website Slashdot. The network presents common features of traditional social networks such as a giant component, small average path length and high clustering, but differs from them showing moderate reciprocity and neutral assortativity by degree. Using Kolmogorov-Smirnov statistical tests, we show that the degree distributions are better explained by log-normal instead of power-law distributions. We also study the structure of discussion threads using an intuitive radial tree representation. Threads show strong heterogeneity and self-similarity throughout the different nesting levels of a conversation. We use these results to propose a simple measure to evaluate the degree of controversy provoked by a post.
Introduction to Stochastic Actor-Based Models for Network Dynamics. Social Networks
, 2009
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Effects of missing data in social networks
- Social Networks
, 2003
"... We perform sensitivity analyses to assess the impact of missing data on the structural properties of social networks. The social network is conceived of as being generated by a bipartite graph, in which actors are linked together via multiple interaction contexts or affiliations. We discuss three pr ..."
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Cited by 80 (1 self)
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We perform sensitivity analyses to assess the impact of missing data on the structural properties of social networks. The social network is conceived of as being generated by a bipartite graph, in which actors are linked together via multiple interaction contexts or affiliations. We discuss three principal missing data mechanisms: network boundary specification (non-inclusion of actors or affiliations), survey non-response, and censoring by vertex degree (fixed choice design), examining their impact on the scientific collaboration network from the Los Alamos E-print Archive as well as random bipartite graphs. The simulation results show that network boundary specification and fixed choice designs can dramatically alter estimates of network-level statistics. The observed clustering and assortativity coefficients are overestimated via omission of affiliations or fixed choice thereof, and underestimated via actor non-response, which results in inflated measurement error. We also find that social networks with multiple interaction contexts may have certain interesting properties due to the presence of overlapping cliques. In particular, assortativity by degree does not necessarily improve network robustness to random omission of nodes as predicted by current theory.
Clustering in Weighted Networks
- Social Networks
"... In recent years, researchers have investigated a growing number of weighted networks where ties are differentiated according to their strength or capacity. Yet, most network measures do not take weights into consideration, and thus do not fully capture the richness of the information contained in th ..."
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Cited by 54 (0 self)
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In recent years, researchers have investigated a growing number of weighted networks where ties are differentiated according to their strength or capacity. Yet, most network measures do not take weights into consideration, and thus do not fully capture the richness of the information contained in the data. In this paper, we focus on a measure originally defined for unweighted networks: the global clustering coefficient. We propose a generalization of this coefficient that retains the information encoded in the weights of ties. We then undertake a comparative assessment by applying the standard and generalized coefficients to a number of network datasets. Key words: clustering, transitivity, weighted networks We wish to give very special thanks to Filip Agneessens, Stephen Borgatti, Carter Butts, and Tom Snijders for their valuable feedback on earlier versions of this paper. We are also grateful to participants of the 3 rd Conference on Applications of Social Network
Main-memory triangle computations for very large (sparse (power-law)) graphs
- Theor. Comput. Sci
"... Finding, counting and/or listing triangles (three vertices with three edges) in massive graphs are natural fundamental problems, which received recently much attention because of their importance in complex network analysis. We provide here a detailed survey of proposed main-memory solutions to thes ..."
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Cited by 44 (0 self)
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Finding, counting and/or listing triangles (three vertices with three edges) in massive graphs are natural fundamental problems, which received recently much attention because of their importance in complex network analysis. We provide here a detailed survey of proposed main-memory solutions to these problems, in an unified way. We note that previous authors paid surprisingly little attention to space complexity of main-memory solutions, despite its both fundamental and practical interest. We therefore detail space complexities of known algorithms and discuss their implications. We also present new algorithms which are time optimal for triangle listing and beats previous algorithms concerning space needs. They have the additional advantage of performing better on power-law graphs, which we also detail. We finally show with an experimental study that these two algorithms perform very well in practice, allowing to handle cases which were previously out of reach. 1 Introduction. A triangle in an undirected graph is a set of three vertices such that each possible edge between them is present in the graph. Following classical conventions, we call finding, counting and listing the problems of
Network reachability of real-world contact sequences
- Physical Review E
, 2005
"... We use real-world contact sequences, time-ordered lists of contacts from one person to another, to study how fast information or disease can spread across network of contacts. Specifically we measure the reachability time—the average shortest time for a series of contacts to spread information betwe ..."
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Cited by 34 (3 self)
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We use real-world contact sequences, time-ordered lists of contacts from one person to another, to study how fast information or disease can spread across network of contacts. Specifically we measure the reachability time—the average shortest time for a series of contacts to spread information between a reachable pair of vertices (a pair where a chain of contacts exists leading from one person to the other)—and the reachability ratio—the fraction of reachable vertex pairs. These measures are studied using conditional uniform graph tests. We conclude, among other things, that the network reachability depends much on a core where the path lengths are short and communication frequent, that clustering of the contacts of an edge in time tend to decrease the reachability, and that the order of the contacts really do make sense for dynamical spreading processes.
Scaling laws of human interaction activity.
- Proc. Natl. Acad. Sci. USA
, 2009
"... Even though people in our contemporary technological society are depending on communication, our understanding of the underlying laws of human communicational behavior continues to be poorly understood. Here we investigate the communication patterns in 2 social Internet communities in search of sta ..."
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Cited by 27 (2 self)
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Even though people in our contemporary technological society are depending on communication, our understanding of the underlying laws of human communicational behavior continues to be poorly understood. Here we investigate the communication patterns in 2 social Internet communities in search of statistical laws in human interaction activity. This research reveals that human communication networks dynamically follow scaling laws that may also explain the observed trends in economic growth. Specifically, we identify a generalized version of Gibrat's law of social activity expressed as a scaling law between the fluctuations in the number of messages sent by members and their level of activity. Gibrat's law has been essential in understanding economic growth patterns, yet without an underlying general principle for its origin. We attribute this scaling law to long-term correlation patterns in human activity, which surprisingly span from days to the entire period of the available data of more than 1 year. Further, we provide a mathematical framework that relates the generalized version of Gibrat's law to the long-term correlated dynamics, which suggests that the same underlying mechanism could be the source of Gibrat's law in economics, ranging from large firms, research and development expenditures, gross domestic product of countries, to city population growth. These findings are also of importance for designing communication networks and for the understanding of the dynamics of social systems in which communication plays a role, such as economic markets and political systems. growth | Gibrat's law | long-term correlations | memory | network growth T he question of whether unforeseen outcomes of social activity follow emergent statistical laws has been an acknowledged problem in the social sciences since at least the last decade of the 19th century (1-4). Earlier discoveries include Pareto's law for income distributions (5), Zipf's law initially applied to word frequency in texts and later extended to firms, cities and others (6), and Gibrat's law of proportionate growth in economics (7-9). Social networks are permanently evolving and Internet communities are growing more each day. Having access to the communication patterns of Internet users opens the possibility to unveil the origins of statistical laws that may lead us to the better understanding of human behavior as a whole. In this paper, we analyze the dynamics of sending messages in 2 Internet communities in search of statistical laws of human communication activity. The first online community (OC1) is mainly used by the group of men who have sex with men (MSM). * The data consists of over 80,000 members and more than 12.5 million messages sent over the course of 63 days. The target group of the second online community (OC2) is teenagers (10). The data covers 492 days of activity with more than 500,000 messages sent among almost 30,000 members. Both web sites are also used for social interaction in general. All data are completely anonymous, lack any message content, and consist only of the times at which the messages are sent and the identification numbers of the senders and receivers. The act of writing and sending messages is an example of an intentional social action. In contrast to routinized behavior, the actants are aware of the purpose of their actions (2, 3). Nevertheless, the emergent properties of the collective behavior of the actants are unintended. In Results Growth in the Number of Messages The cumulative number m j (t) expresses how many messages have been sent by a certain member j up to a given time t [for better readability, we will not write the index j explicitly, m(t); see details on the notation in the SI Appendix, Sec. I]. The dynamics of m(t) between times t 0 and t 1 within the period of data acquisition T (t 0 < t 1 ≤ T) can be considered as a growth process, where each member exhibits a specific growth rate r j (r for short notation): where m 0 ≡ m(t 0 ) and m 1 ≡ m(t 1 ) are the number of messages sent until t 0 and t 1 , respectively, by every member. To characterize the dynamics of the activity, we consider 2 measures. (i) The conditional average growth rate, r(m 0 ) , quantifies the average growth of the number of messages sent by the members between t 0 and t 1 depending on the initial number of messages, m 0 . In other words, we consider the average growth rate of only those members who have sent m 0 messages until t 0 (see Materials and Methods for more details). (ii) The conditional standard deviation of the growth rate for those members who have sent m 0 messages until t 0 , σ(m 0 ) ≡ (r(m 0 ) − r(m 0 ) ) 2 , expresses the statistical spread or fluctuation of growth among the members depending on m 0 . Both quantities are relevant in the context of Gibrat's law in economics (7-9) which proposes a proportionate growth process, entailing the assumption that the average and the standard deviation of the growth rate of a given economic indicator are constant and independent of the specific indicator value. That is, both r(m 0 ) and σ(m 0 ) are independent of m 0 (9). In
Core-periphery organization of complex networks
- Physical Review E
, 2005
"... Networks may, or may not, be wired to have a core that is both itself densely connected and central in terms of graph distance. In this study we propose a coefficient to measure if the network has such a clear-cut coreperiphery dichotomy. We measure this coefficient for a number of real-world and mo ..."
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Cited by 26 (3 self)
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Networks may, or may not, be wired to have a core that is both itself densely connected and central in terms of graph distance. In this study we propose a coefficient to measure if the network has such a clear-cut coreperiphery dichotomy. We measure this coefficient for a number of real-world and model networks and find that different classes of networks have their characteristic values. For example do geographical networks have a strong core-periphery structure, while the core-periphery structure of social networks (despite their positive degree-degree correlations) is rather weak. We proceed to study radial statistics of the core, i.e. properties of the n-neighborhoods of the core vertices for increasing n. We find that almost all networks have unexpectedly many edges within n-neighborhoods at a certain distance from the core suggesting an effective radius for non-trivial network processes.