For this milestone, due in Module Three, you will submit a draft of the literature review due as part of your final research investigation using the three articles that were provided for your track and topic in Module Two

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For this milestone, due in Module Three, you will submit a draft of the literature review due as part of your final research investigation using the three articles that were provided for your track and topic in Module Two. In addition, for this milestone, you will need to find two additional articles to use for your final project. You will base this milestone on the literature review practice journal assignment that you completed in Module Two. Rather than following the format of a typical lengthier APA literature review, you will instead prepare five shorter, adapted, individual literature reviews (one for each article). Each literature review should be one page in length (all five should be submitted as one five-page document). These literature reviews will lead up to the final literature review submission, which will consist of a total of five literature reviews, based on the three articles provided in your track and two more articles found and selected by you for this milestone task. The final version of the literature review will be submitted in Module Seven as part of Final Project Part I.

Prompt

First, read and review the three articles for your track. Next, using the questions presented in the Module Two literature review practice journal assignment as a guide, you will draft three literature reviews of the articles provided in your track. You will then find two more articles to add to your literature reviews. The questions are provided here for your convenience. These questions will support you in completing the literature reviews, which will need to address all of the critical elements below.

Socio-spatial Properties of Online Location-based Social Networks Salvatore Scellato Anastasios Noulas Computer Laboratory University of Cambridge salvatore.scellato@cam.ac.uk Computer Laboratory University of Cambridge anastasios.noulas@cl.cam.ac.uk Renaud Lambiotte Cecilia Mascolo Deparment of Mathematics Imperial College London r.lambiotte@imperial.ac.uk Computer Laboratory University of Cambridge cecilia.mascolo@cl.cam.ac.uk Abstract The spatial structure of large-scale online social networks has been largely unaccessible due to the lack of available and accurate data about people’s location. However, with the recent surging popularity of location-based social services, data about the geographic position of users have been available for the first time, together with their online social connections. In this work we present a comprehensive study of the spatial properties of the social networks arising among users of three main popular online location-based services. We observe robust universal features across them: while all networks exhibit about 40% of links below 100 km, we further discover strong heterogeneity across users, with different characteristic spatial lengths of interaction across both their social ties and social triads. We provide evidence that mechanisms akin to gravity models may influence how these social connections are created over space. Our results constitute the first largescale study to unravel the socio-spatial properties of online location-based social networks. Introduction Online Location-based Social Networks (LBSNs) have recently attracted millions of users, experiencing a huge popularity increase over a short period of time. Thanks to the widespread adoption of location-sensing mobile devices, users can share information about their location with their friends. Among the biggest providers there are Foursquare and Gowalla, while other hugely popular social networking services such as Facebook and Twitter have also introduced location-based features. Location is increasingly becoming a crucial facet of many online services: people appear more willing to share information about their geographic position with friends, while companies can customize their services by taking into account where the user is located. As a consequence, service providers have access to a valuable source of data on the geographic location of users, as well as to online friendship connections among them. The combination of these two factors offers a groundbreaking opportunity to understand and exploit the spatial properties of the social networks arising among online users, but also a potential window on real human socio-spatial behavior. Copyright c 2011, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. Spatial networks have been extensively studied, particulary when dealing with transportation and mobility networks, Internet router connections, power grids, urban road networks and other systems where nodes are embedded in a metric space (Barthe?lemy 2011). In general, metric distance directly influences the network structure of such systems by imposing higher costs on the connections between distant entities. Social networks, instead, have been largely studied from a purely topological perspective, focusing on the structural position of their nodes and on structural mechanisms that describe their evolution. Sociologists have studied the effect of distance on social ties with the underlying assumption that most individuals try to minimize the efforts to maintain a friendship link by interacting more with their spatial neighbors (Mok, Wellman, and Carrasco 2009; Goldenberg and Levy 2009). Nonetheless, the connection cost that heavily affects other types of spatial networks may not be as important in social systems, particularly when focusing on online interactions. As proposed by Cairncross (2001), distance may cease to play a role because of the increasing availability of affordable longdistance travel and new communication media, resulting in the inevitable “Death of Distance”. Social Ties and Geographic Distance One fundamental spatial property of social networks is the probability P (d) of having a social connection between two individuals as a function of their distance d. Even though there is universal agreement on the fact that P (d) decreases with distance, the exact relationship between these two variables is still unclear. Lambiotte et al. (2008) have found that it decays as P (d) ∼ d−2 in a mobile phone communication network, while Liben-Nowell et al. (2005) have found a different relationship P (d) ∼ d−1 + among online bloggers on LiveJournal in the USA, being a constant probability which acts on online communities regardless of distance. In another study, Backstrom et al. (2010) have similarly found spatial scaling P (d) ∼ 1/d among online interactions: they show how this association appears so strong and important that it can be safely exploited to infer where Facebook users are only from the location of their friends (Backstrom, Sun, and Marlow 2010). It has also been proposed that the spatial structure of social networks might be scale-invariant, with a universal distribution P (d) ∝ d−1 (Hu et al. 2011): nonetheless, the exact nature of this relationship in a spatial social network often conveys interesting information about how geographic distance constrains social ties. At the same time, the effect of online communication tools on such relationship is still under debate, even though initial results tend to confirm that distance is still an important factor that shapes human online interaction, with some individuals engaging preferentially with spatially close acquaintances across different online and offline communication media (Mok, Wellman, and Carrasco 2009; Goldenberg and Levy 2009; Scellato et al. 2010). Analysis of Location-based Services Location-based social platforms represent the ideal systems to investigate the spatial properties of social networks arising among online users for three main reasons. First of all, they uniquely provide data on both social connections and geographic locations, making socio-spatial analysis possible. Then, user location information in these services is often more accurate than text-based descriptions usually available in other online systems (Hecht et al. 2011), as it is acquired through sensing devices whenever users willingly check-in, that is when they share with their friends information about the place where they are. Finally, they have quickly accumulated hundreds of thousands, and sometimes millions, of users, thus enabling large-scale studies which can uncover general properties and trends. Among the many research questions that arise, apart from the fundamental one about understanding the effect of distance on online relationships, there is the need to understand whether space homogeneously affects users or if, instead, some individuals prefer connecting to people further away, leading to a heterogeneous system. Moreover, social networks are often characterized by a large number of social clusters, where triads of individuals are mutually connected. Although social triangles seem to generally appear across different geographic scales (Lambiotte et al. 2008), different users may exhibit varied preferences towards short-range or long-distance triads (Scellato et al. 2010). Spatial Properties of Online Social Networks We will address these questions by analyzing three different popular LBSNs: Brightkite, Foursquare and Gowalla. We have collected data about all of them and extracted the social networks among their users. We are able to assign a “home location” to each user, in order to embed the nodes in a 2dimensional metric space. Then, we design two randomized null models of a spatial network which allow us to investigate the statistical significance of the empirical properties found in these networks. We observe heterogeneity in the characteristic distance of interaction across users, with some of them exhibiting preference towards short-range rather than long-distance ties. In addition, we study the geographic properties of social triads. Again, we find non-trivial heterogenities across users, with some of them belonging mainly to geographically small triads and others to wider ones, spanning thousands of kilometres. In particular, users with more friends tend to create triangles with individuals further apart far more than expected by chance. We discuss how user heterogeneity seems compatible with mechanisms akin to gravity models, with the likelihood of connection between two users depending both on their popularity (i.e., number of friends) and on their distance. This work constitutes the first large-scale study to investigate the spatial structure of online LBSNs, observing robust and universal properties across three of these social services: the observed features may be the signature of social processes happening regardless of the particular online tool adopted by users. While previous research has been focusing on defining new measures to take geographic distance into consideration when dealing with social networks (Scellato et al. 2010) and on exploiting simple socio-spatial properties to predict user location (Backstrom, Sun, and Marlow 2010), our contributions are different: we shed new light on how these socio-spatial properties arise from social and spatial factors and how user heterogeneity is related to both of these aspects. We believe location-based features will become ubiquitous in online social services: our findings may then inspire how systems and applications are designed and implemented on these services. Data Collection In this work we study three spatial social networks acquired from different popular online location-based social services. We extract the social networks arising among users and a single geographic home location for each user. Brightkite Brightkite was founded in 2007 as a social networking website which allows users to share their location with their friends: it is available worldwide and it is based on the idea of making check-ins at places, where users can see who is nearby and who has been there before. Brightkite users can establish mutual friendship links and they can push their check-ins to their Twitter and Facebook accounts. We study a dataset collected in September 2009 which includes the whole Brightkite user base at that time, with information about 54,190 users (Scellato et al. 2010). Since this dataset was collected, Brightkite has gathered more than 2 millions members: nonetheless, this dataset represents a complete snapshot of a popular location-based service in its initial evolution phase. Foursquare Foursquare was created in 2009 and it has quickly risen as the most popular location-based service, with more than 6 million users as of January 2011. Users utilize the Foursquare application on their mobile devices, which allows them to check-in, sharing with their friends the place where they are. Foursquare provides game features, since the user with the highest number of check-ins in the last 60 days becomes the mayor of a place. Acquiring Foursquare data requires user authorization to collect personal information and has rate limitations set in place. However, many Foursquare users choose to automatically push their check-in messages to Twitter, which provides a public API to search and download these messages. Dataset Brightkite Foursquare Gowalla N 54,190 258,706 122,414 K 213,668 2,854,957 580,446 NGC 50,896 254,532 117,361 hki 7.88 22.07 9.48 hCi 0.181 0.191 0.254 DEF F 5.73 5.90 5.44 hDi 5,651 8,494 5,663 hli 2,041 1,442 1,792 Table 1: Properties of the datasets: number of nodes N and edges K in the social network, number of nodes in the giant connected component NGC , average node degree hki, average clustering coefficient hCi, 90-percentile effective network diameter DEF F , average geographic distance between nodes hDi [km], average link length hli [km]. 100 Brightkite Foursquare Gowalla CCDF 10−1 10−2 10−3 10−4 10−5 10−6 0 10 101 102 Degree 103 104 Figure 1: Empirical Complementary Cumulative Distribution (CCDF) of the number of friends in Brightkite, Foursquare and Gowalla. The inset shows the same distributions rescaled by dividing for the average number of friends in each network: the three datasets fall on the same curve. Thus, we have recorded approximately 4 million tweets, each one containing a check-in sourced by a Foursquare user during June 2010. Those messages come from about 250,000 different users and cover about 1.5 million locations on the planet. We estimate that our sample contains approximately 20% to 25% of the entire Foursquare user base at collection time. Each tweet provides a URL to the Foursquare website, where information about the geographic location of the venue can be acquired. Since Foursquare does not provide unathorized access to user friends list, we have acquired friendship ties that Foursquare users have among them on Twitter, where they are publicly available, extracting a social network. While the resulting social graph is not expected to be identical to the original Foursquare graph, it provides a reasonable approximation and we will show how it conveys meaningful information, comparable to the other datasets. Finally, we extract as home location of each user the geographic location of the place where he/she has more check-ins overall. Gowalla Gowalla is a location-based social network created in 2009: its users check-in at places through their mobile devices. Check-ins are shared with friends: as a consequence, friends can check where a user is or has been; conversely, it is possible to see all the users that have recently been in a given place. The friendship relationship is mutual, requiring each user to accept friendship requests to allow location sharing. However, there is a small number of user accounts that represent companies or other organizations and appear to automatically accept every friendship request. These accounts can become hugely popular and collect thousands of connections. Gowalla provides a public API to let other applications integrate with their service: in particular, they provide information about user profiles, friend lists, user check-ins and place details. We have collected a complete snapshot of Gowalla data in August 2010. For every user we have gathered the user profile, the friends list and the list of all the check-ins the user has made. Finally, for each place we have collected its geographic location, as specified in Gowalla, described as a latitude-longitude pair. Since users are identified by consecutive numeric IDs, we were able to exhaustively query all user accounts. As in Foursquare, we define the home location of each user as the place with the largest number of check-ins. Network Socio-spatial Properties We first address the spatial properties of the social networks under analysis, focusing on the main topological and geographic measures. We discuss the fundamental relationship between likelihood of friendship and geographic distance and, finally, we define two randomized spatial networks models which will help later assessing the statistical significance of the properties we observe in these systems. Socio-spatial properties More formally, a spatial social network is a social network whose actors are positioned in a space equipped with a metric (Barthe?lemy 2011). In our case, online users are located over the 2-dimensional surface of the Earth and we adopt the great-circle distance as metric: the distance Dij between any two nodes i and j is then computed given their geographic coordinates. Then, the social network can be represented as an undirected graph G with N nodes and K links, with users as nodes and where a link exists for each social tie (e.g., a person lists another user as one of his/her friends). We associate a length lij to each social link so that lij = Dij . The general properties of these three datasets are reported in Table 1. The social networks are heterogeneous in size, ranging from 54,190 nodes in Brightkite to 258,706 in Foursquare; the average degree is lower in Brightkite and Gowalla, respectively 7.88 and 9.48, than in Foursquare, where users have on average 22.07 friends. Thus, Foursquare presents a much denser and bigger social network, a consequence of its dominance of the LBSN market. All networks present a giant connected component which contains the vast majority of the users. The degree distributions for the three networks are reported in Figure 1: CDF 0.8 Brightkite Foursquare Gowalla Probablity of friendship 1.0 0.6 0.4 0.2 0.0 100 Friends Users 10 1 2 3 10 10 Distance [km] 10 4 10 5 Figure 2: Empirical Cumulative Distribution (CDF) of the geographic distance between all users (dotted line) and between connected friends (solid line) for the three datasets. they all show a heavy-tail, with some users having thousands of friends. Rescaling the degree distributions by their average values results in a common trend, as shown in the inset. These networks also exhibit high values of average clustering coefficient, between 0.18 and 0.26, and short topological distances among their nodes, with 90% of all couples being less than 6 hops away. These properties confirm the smallworld nature of LBSNs, as found in other online social systems (Leskovec and Horvitz 2008). The average geographic distance between users hDi is consistently larger than the average distance between friends hli across all the datasets: while the first value ranges between 5,600 and 8,500 km, the latter has much shorter values, between 1,400 and 2,000 km. This already provides evidence that the probability of having a social link between two users decreases with distance: we will further investigate this relationship later. The distribution of social link length is comparable across the three datasets, as shown in Figure 2: about 40%-50% of all couples of friends are within 100 km, with more than 3% of all links being shorther than 1 km. Instead, the distribution of distances among users, also shown in Figure 2, has a different behavior: about 50% of users are at distances larger than 4,000 km across all the networks. Online Friendship and Distance To further investigate how social links appear more likely to exist between close rather than distant users, we study the probability of friendship P (d) as a function of distance d by counting Ld , the number of social links with length d, and by estimating Nd , the number of pairs of users at distance d. This gives us P (d) = L(d)/N (d). As discussed before, this relationship has been found to be close to a law P (d) ∼ d−α , with values of α ranging between 1 and 2 (Liben-Nowell et al. 2005; Lambiotte et al. 2008; Backstrom, Sun, and Marlow 2010; Goldenberg and Levy 2009). As shown in Figure 3, our datasets present noisy patterns and, furthermore, Brightkite and Gowalla exhibit an almost flat probability in the range 1-10 km, while all curves then decrease as distance grows and then they reach another steady probability between 1,000 and 4,000 km, maybe denoting a background probability that affects individuals 10−2 α = 0.5 10−3 10−4 10−5 10−6 0 10 Brightkite Foursquare Gowalla 10 1 α = 1.0 102 Distance [km] 103 104 Figure 3: Probability of friendship between two users as a function of their geographic distance for the three datasets under analysis. The two straight lines represent probability P (d) ∼ d−α with two different exponents α = 0.5 and α = 1.0. within this distance threshold. Similar constant trends at short and long geographic ranges have also been found in other online systems (Backstrom, Sun, and Marlow 2010; Liben-Nowell et al. 2005). The appearance of social