File-Sharing Preference in a Peer-to-Peer Network

Feature

File-Sharing Preference in a Peer-to-Peer Network Yipeng Li, Yong Ren, Jian Yuan, and Xiuming Shan

Abstract

Digital Object Identifier 10.1109/MCAS.2010.939784 Date of publication: 18 February 2011

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Peer-to-peer network describes a typical complex network upon which users connect together according to their sharing preference, indicated by the resources they shared. In this article, we apply analytic methods from complex networks theory to investigate the sharing preference of users as well as the correlations between different resource categories in a real peer-to-peer file sharing system, which is helpful for getting more insight into rapid development of peer-to-peer network applications.

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P2P network is usually considered as a communication system, in which users connect together through certain data transmission channels. network, to find the structural information among connected users and to model and design application protocols. For instance, the typical scale-free connectivity is revealed in Gnutella-like systems [9]–[12], and various rewiring methods [13], [14] were introduced into modeling their topological structures. Moreover, the compromise between structural simplicity and search efficiency [15]–[23], and the relation between underlying network structure and traffic, has been studied as well [24]–[29]. Dealing with the system from the binary perspective, however, some important inherent factors for understanding P2P application complexity are generally neglected. Data-sharing graph [30], in which users connect together according to the resources they shared, can capture some common sharing preference of users. Still limited within the unweighted structure, the smallworld properties were analyzed but only for three datadistribution systems [30]. Unfortunately, what the specific sharing preference is, whether and how resources are correlated via users and the correlation extent, etc., were not discussed [30]. On the contrary, the analysis of biding activity in eBay [31] brings us more inspiration. Bidders connect and bid items correlated to the opposite sides in the form of a bipartite structure, with weighted edges indicating the interaction strengths among them. Based on the clusters identified, the correlation level of different categories can be explored. Nevertheless, bidding preference of bidders is not studied in depth there [31]. Moreover, what the specific weights are, what the inherent cluster structure is in the case where specific weights are considered, and which individual preference we can get through these clusters,

Users

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Figure 1. Bipartite sharing graph between users and resources.

etc., are still needed to answer for better understanding of this kind of system. In this article, we investigate the fingerprint-sharing preference of users as well as the correlations between different resource categories in a real P2P file sharing system. Based on empirical data, we reveal that various resource categories are strongly correlated due to users’ sharing behaviors. In particular, we find that the sharing preference of users corresponds to specific resource subcategories. The rest of the article is organized as follows: Firstly, we model weighted user network and resource network, and identify the weighted clusters in these two networks. We then study resources closeness in the resource cluster and consequently measure users’ sharing preference in the user cluster. Finally, a brief conclusion will be drawn. II. Weighted User Network and Resource Network Our study is based on the empirical data collected from a real P2P application, “byrBT” in CERNET (China Education and Research NETwork), which is a BitTorrentlike file-sharing system. The dataset contains 81531 downloading logs from October 20 to 31, 2009, and there was a total of 10368 users and 7376 different resource files included. Each item in the downloading logs indicates what specific resource the user has downloaded with his unique ID. After that, the user can upload the resource for other users. This implies the sharing interest of the user to that particular resource. This kind of relation between the users and the resources could be described by a bipartite sharing graph, with one subset for the users and the other for the resources, as illustrated by Fig. 1. In the figure, edges indicate the sharing interests of the user to the resource, for example user “A” is interested in resource “a,” so are users “B” and “E”; moreover, users “A,” “C” and “E” have common interest in resource “b.” This bipartite sharing graph highlights the interrelation among various users and resources. On one hand, connections from a certain resource to several users imply their common sharing demand. In Fig. 2(a), for example, users “A” and “B” share the same resource “a,” “A” and “E” are both interested in three common resources: “a,” “b” and “e.” Based on this, we could

Yipeng Li, Yong Ren, Jian Yuan and Xiuming Shan, Department of Electronic Engineering, Tsinghua University, Beijing 100084, China. E-mail: yp-li05@ mails.tsinghua.edu.cn

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generate a weighted user network to describe the interest similarity among users, as shown in Fig. 3(a). In this figure, “A” and “B” have a unit-weight edge for sharing resource “a,” “A” and “E” have three common sharing demands, for “a,” “b” and “e,” with a weight-3 edge. On the other hand, connections from a certain user to several resources make these resources correlated thereby constituting a weighted resource network, which also reveals the user’s diverse sharing preferences. For instance, in Fig. 2(b), resources “a” and “c” are correlated to “B” via sharing, which corresponds to the unitweight edge between them in Fig. 3(b). Resources “a” and “e” are simultaneously shared by “A” and “E,” having a weight-2 edge in between. A weighted adjacency matrix WA 5 3 wij 4 is used to represent these two weighted networks, wij in position (i, j ) indicates the weight of the edge that connects nodes i and j , wij 5 0 if i and j are unconnected. The weight of node i is denoted as wi 5 a wij j

(1)

It merely is the sum of weights of the edges attached to it. For a network having N nodes, the average node weight can be described as 8w9 5

a i wi N

(2)

In addition, the clustering coefficient c is introduced to measure the node connection density. Clustering coefficient of node i is [32] ci 5

2ti 1 di di 2 1 2

(3)

where ti is the number of triangles centered at node i, and dj is the degree of node i. Moreover, the clustering coefficient of the whole network is a ici (4) c5 N The basic information of these two weighted networks is summarized in Table 1. The weighted user network and resource network together provide more information about users and resources of the P2P network. Users are connected together via resources, capturing different sharing preferences, and the resources are correlated due to users’ sharing behaviors. Weighted edges indicate the interaction strength among users and resources. With specific resources categories information included, the user sharing preference tendency and the detailed resource correlation could be revealed based on the FIRST QUARTER 2011

A

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a (a)

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Figure 2. Users sharing common interest (a) and resources correlation (b).

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Figure 3. Weighted user network (a) and weighted resource network (b). Numbers indicate the weights of the thick edges, while other edges have a unit weight.

network structure, which is different from the binary one by nature. III. Weighted Clusters Identification The hierarchical structure of weighted user network and resource network is analyzed in this section. Usually, researchers study the topological structure of a network according to the connection relation [33], [34], which contain information about nodes connection. Fig. 4(a) illustrates a binary or unweighted network, in which A, B, C, D are fully connected with two leaf nodes E and F. Obviously, the fully connected nodes are connected densely and intuitively belong to the same cluster covered by a shadow region in the figure. Considering edges with weights indicating interaction strengths, called interaction relation here, the situation is somewhat different as depicted in Fig. 4(b). In this figure, B and C are clustered together via a weight-4 edge, interacting stronger than that in the binary network, so are A, E and D, F. One can clearly see that interaction relation could provide more internal structural information of the network. Table 1. The numbers of nodes N, edges L, average weight of node and cluster coefficient c for weighted user and resource networks. N L c User Network 10 368 422 388 24.34 0.5275 Resource Network 7 376 218 560 24.13 0.5866 IEEE CIRCUITS AND SYSTEMS MAGAZINE

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C

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(b)

Figure 4. Distinct structure with differentiating connectivity relation (a) and interaction relation (b).

where eii indicates the fraction of edges with both endnodes in cluster i, and ai is the fraction of edges where one or both end-nodes are in cluster i. In a corresponding fast algorithm [38], the update matrix DQ is used to save minor increment of Q, suggesting the best possible cluster identification once reaching the maximum. Here, we further develop DQ for weighted user network and resource network, as follows: wij DQ 5 • 2mw 0

Furthermore, weighted edges in the user network indicate the heterogeneity of users’ sharing preferences, more than just the simple interaction strengths among them. Here, the interaction relations among users are mapped onto multigraphs [35], having multiple edges corresponding to the edges with weights larger than unity. For example, Fig. 5(a) describes an original weighted user network, Fig. 5(b) shows the corresponding multigraphs, and Fig. 5(c) indicates the multiple edges with detailed information. Users “A” and “B” built a weight-2 edge for sharing two movie resources, showing the “depth” in sharing preference between them; that “A” and “C” have a weight-3 edge due to movie, game and comic files, indicating the “width” of their preference. With resource categories considered, such multigraphs are very helpful to obtain more details about users’ sharing preferences, which will be further discussed in the following section. In complex networks and other interdisciplines, such as social networks in particular, many clustering algorithms for classical binary networks have been proposed based on the modularity parameter Q [ 1 0, 1 2 [33], [36], [37], defined as

Q 5 a i 1 eii 2 a2i 2 B

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D (b)

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wiwj 1 2mw 2 2

if wij 2 0

(6)

otherwise

where wij is the weight of edge from i and j, wi is the weight of i, mw 5 wi is the sum of all node weights. Initially, each node is set to be a single cluster. Then, elements are selected pairwise from the weighted adjacency matrix WA to calculate the matrix DQ, accumulating the largest item among all of the DQ onto Q and then clustering the corresponding two nodes together. This procedure is repeated till Q reaches maximum. Figure 6(a) shows the increment of Q while nodes are clustered together. We find that the modularity parameter Q 5 0.7443 for the user network and Q 5 0.6474 for the resource network, showing that both of them are well clustered [33]. There is a total of 461 and 494 distinct clusters in the user network and the resource network, respectively, without a uniform cluster size, as shown in Fig. 6(b). In the user network and the resource network, several clusters contain a large number of nodes, but the majority of clusters have fewer ones. Moreover, there are still 291 isolated users and 288 isolated resources, which have no connections with the others.

IV. Resources Closeness in Resource Cluster Resources may belong to different resource categories, specific resource files are correlated together due to a sin(5) gle user’s downloading. Meanwhile, many users sharing to the same resource collections indicates the closeness of different B resource categories, which appear ie ov to be independent of each other M ovie Movie A M in terms of their names or types. Game C C In this section, we investigate the omic So ftw correlation of different resource ar D e categories based on the clustering structure of the network. (c)

Figure 5. Multigraphs of the weighted user network. The original weighted network of A, B, C, and D is as in (a), mapped onto multigraphs in (b), with specific resource categories considered in (c).

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A. Resource Categories To facilitate the following analysis, it is necessary to first categorize FIRST QUARTER 2011

Users sharing behaviors indicates the closeness of different resource categories, which appear to be independent of each other in terms of their names or types.

1.0 User Network Source Network

0.8 0.6 Q

B. Resources Closeness Obviously, the clusters we obtained are not completely equivalent to the nine categories or 355 subcategories shown above. Thus, our goal is to find the internal closeness among various resource subcategories, not limited to the categories level, for more preciseness. To illustrate the concept of closeness, we select several clusters according to their ranks of cluster sizes, and classify the resources within the clusters into 355 subcategories, while the comparison of each subcategory proportion will indicate the closeness. Figure 7 shows the proportion (on the y-axis) of all subcategories (on the x-axis) in clusters 2, 6, 13, and 17, respectively, with a sharing ratio of each subcategory introduced for reference – the larger the grey degree is, the bigger the sharing ratio or the more popular the subcategory is. Clearly, all these clusters contain the majority of subcategories with different proportions. Here, we say some subcategories are close if they have a relatively large and similar proportion within the same cluster. For example, Fig. 7 shows three relatively more popular subcategories: the story and love movies (a), Chinese music (b), and PC online games (c), are closer in cluster 2 than in the others, so are the American dramas (e) and music videos (f) in cluster 17, implying that these popular subcategories meet the majority of users’ sharing preference. On the other hand, some less popular subcategories, such as the foreign language study materials (d) in cluster 13, is somewhat far away from the others. Nevertheless, the cluster arising indicates that resources belonging to (d) are frequently shared by some users with special interests.

V. Users’ Sharing Preference In User Cluster Users’ sharing preference is the main factor that influences the evolution of the P2P network. Users interact with different strengths via their sharing behaviors to the resources, and they cluster together due to their common sharing preference. For a single user cluster, the resource subcategories that have been shared provide more detailed information and characterize the specificity of users’ sharing preference. This important notion is discussed in the present section.

0.4 0.2 0.0 0

9,000 3,000 6,000 Number of Clustered Nodes (a)

12,000

104 User Network Source Network

103 Cluster Size

the involved resources. There are a total of 7376 different resources, which can be divided into nine categories according to the traditional classification scheme used in the “byrBT” system, each having several subcategories to sum up to a total of 355, as shown in Table 2. Due to the self-organized uploading behaviors of users, 291 resources cannot be categorized correctly, account for 3.95%.

102 101

100 100

101 102 Rank of Cluster Size (b)

103

Figure 6. Q increases with the nodes clustered (a). Cluster size in the weighted user network and resource network (b).

Table 2. The number of source subcategories in each category. Category Subcategories Number FIRST QUARTER 2011

Movie 114

TV Drama 17

Music 29

Game 12

Comic 24

Variety Shows 16

Software 11

Materials 113

Sports 19

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Resource Categories Proportion

Cluster 4 Cluster 9 Cluster 20 0.4

Sports

p5

a i[C wik . a i[C

0.2

M TV ovie D ra m a M us ic G am e Va C rie om ic ty Sh ow s So ftw M are at er ia ls Sp or ts

0.0

Figure 8. General users’ sharing preferences in clusters 2, 4, 9, and 20, respectively. The x-axis indicates the resource categories, and the y-axis presents the proportion of each category.

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Materials

Comic

Variety Shows Software

Music

Game

TV Drama

Movie

A. Sharing Preference We select several user clusters, Subcategory Sharing Ratio identify the resource categories that have been shared, and calculate the proportion of each categoCluster 2: 865 Sources ry. Figure 8 shows the situations in 0.1 clusters 2, 4, 9, and 20, respective(b) (c) (a) 0.05 ly. Generally, the movie category 0 occupies the largest proportion in these four clusters, indicating Cluster 6: 338 Sources 0.1 a global sharing preference. Us0.05 ers joined in the system for downloading movie files which they 0 are interested in. Besides, there Cluster 13: 119 Sources are other categories that also ac0.4 (d) count for large proportions, such 0.2 as Sports in cluster 2, Variety in 0 cluster 4, TV dramas in cluster 20, Cluster 17: 71 Sources which reveal some differences of 0.2 these clusters. (e) (f) 0.1 To be more precise, we focus 0 on highlighting the specific sharing preferences in some selected clusters, related to resource subcategories. For a single user cluster, users built weighted edges according to their sharing Figure 7. Illustration of resource subcategory closeness in resource clusters. The resources, belonging to various x-axis represents 355 subcategories, and the y-axis indicates the proportion of subcategories. In other words, each subcategory in the selected clusters. (a): story and love movies; (b): Chinese each resource subcategory inmusic; (c): PC online games; (d): foreign language study materials; (e): America troduces a certain proportion of dramas; (f): music videos. edge weights. For example, user i in cluster C has a weight wi, in which wik is introduced by resource subcategory k. Then, the weight proportion p of k among all of the subcategories in cluster C is defined as 0.6 Cluster 2

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(7)

wi

More specifically, wi is the weight of user i, which also means that the number of resources i has shared with the other users. And wik indicates the number of shared resources belonging to subcategory k. Figure 9 illustrates p corresponding to each resource subcategory in the user clusters, similar in style to Fig. 7. Various resource subcategories, not limited to the largest proportion category of movies (corresponding to the situation shown in Fig. 8), exert crucial influence onto p in the selected clusters. In Fig. 10, comedy movies (a) and story movies (e) belonging to the movie category cause the largest p in clusters 2 and 9, FIRST QUARTER 2011

0.5

Cluster 2: 1,112 Users (a) (b) (c)

0 1

Cluster 4: 679 Users (d)

0.5 0 p 1

Cluster 9: 212 Users (e)

0.5 0 1

Cluster 20: 92 Users (f)

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respectively. Meanwhile, cartoon movies (b) and adventure movies (c) also account for large proportions in cluster 2. On the other hand, the Hong Kong and Taiwan variety shows (d), from the category of variety shows, leads to a maximum p in cluster 4, so is the American dramas (f), which belong to TV dramas in cluster 20. This observation implies that these specific resource subcategories are explicit sharing preferences of the users in the corresponding clusters, showing individual characteristics just like human fingerprints. Edge weights introduced by these subcategories make the connections among users denser, which is the crucial factor leading to a different and yet stable cluster structure in the weighted user network.

Figure 9. The proportion p of edge weights introduced by various resource subcategories in user clusters. The x-axis presents the subcategories, and the y-axis B. Structural Evolution denotes p. (a) comedy movies; (b) cartoon movies; (c) adventure movies; (d) Hong The sharing preference of users Kong and Taiwan variety shows; (e) story movies; (f) American dramas. that corresponds to a specific resource subcategory plays a dominant role in the clustering structure of the network. For a single user cluster, we calculate the number of unconnected components when the edge weights introduced by some subcategories are removed. Table 3 shows the situations corresponding to several typical subcategories. When the category of comedy movies is removed, there are 89 unconnected components left in cluster 2, with 77 unconnected components left out corresponding to Adventure (b) (a) movies. Meanwhile, the removal of the Hong Kong and Taiwan variety shows splits cluster 4 into 87 isolated components. Here, we furthermore illustrate the topological evolution of cluster 20, via removing edge weights introduced by comedy movies and American dramas (see Table 3). Figure 10(a) shows the original topology, where thicker edges have heavier weights. First, we remove comedy movies from Fig. 10(b), and the resulting topology appears a little sparse with an isolated user. Then, we (c) (d) remove edge weights introduced by American dramas, Figure 10. Topological evolution of cluster 20, where obtaining a sparser topology with more isolated users as thicker edges have heavier weights. (a) shows the origishown in Fig. 10(c), which causes the maximum p shown nal topology. (b) presents the topology after removing the comedy movie edge weights. (c) indicates the result after in Fig. 9. Finally, we remove the edge weights of these removing the American dramas. (d) is the resulting nettwo subcategories and arrive at a very sparse network, work after eliminating the two subcategories. as shown in Fig. 10(d). FIRST QUARTER 2011

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Table 3. Number of unconnected components left when typical resource subcategories are removed. Cluster 2: 1112 users Story movie Love movie Comedy movie Cartoon movie Adventure movie American drama Hong Kong and Taiwan variety shows Basketball video

89 75 77

Cluster 4: 679 users 4 4 8

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Cluster 20: 92 users

31

3

26 87 4

VI. Conclusions In this article, we have investigated the file-sharing preference of users and correlation between different resource categories in a real peer-to-peer network. Based on the empirical data collected from the “byrBT,” a BitTorrent-like peer-to-peer file-sharing system, we first construct a bipartite sharing graph between users and resources to describe users’ sharing interest for specific resources. We then modeled the weighted user network and resource network. In the weighted user network, users built connections based on their sharing interests to similar resources, and different resources are correlated together due to many users’ sharing behaviors, with weighted edges indicating their interaction strengths. We next identified the clusters in these two weighted networks through considering the edge weights, which provide more inherent structural information different from the classical binary network model. We found that the two networks both show well clustering structures, with several clusters including large numbers of nodes but the majority of clusters having fewer ones. According to the cluster structure, we revealed that various resource subcategories within the same cluster are strongly correlated, apparently different from the conventional classification according to resource names and types. And, more interestingly, we discovered that when the specific weights among users are considered, the filesharing preferences of users within different clusters correspond to specific resource subcategories just like human fingerprints, which play a dominant role in the clustering structure of the underlying network. We finally showed that the users’ connectivity decreases prominently with the corresponding subcategories removed, resulting in a sparse topological structure. Based on these observations and analysis, we believe that the resource servers can be configured more efficiently in practical application systems, such as P4P [39], to name just a typical one. 50

Cluster 9: 212 users 38

VII. Acknowledgments This work was partly supported by the National Nature Science Foundation under Grant No. 60932005, and National Basic Research Program of China (973 Program) under Grants No. 2007CB307100, 2007CB307105. Yipeng Li is a Ph.D. candidate in the Department of Electronic Engineering at Tsinghua University, Beijing, China. He received his B.S. and M.S. degrees in electronics engineering from Harbin Institute of Technology, China, in 2003 and 2005, respectively. His research interests include complex systems theory and Internet applications analysis. Yong Ren received his B.S, M.S and Ph.D. degrees in electronic engineering from Harbin Institute of Technology, China, in 1984, 1987, and 1994, respectively. He worked as a post doctor at the Department of Electronics Engineering, Tsinghua University, Beijing, China, from 1995 to 1997. Currently he is a professor of EE Department and the director of the Complexity Engineered Systems Lab (CESL) in Tsinghua University. He holds 12 patents, and has authored or coauthored more than 100 technical papers in behavioral analysis of computer networks, P2P networks and wireless communication networks. He serves as reviewer for the IEICE Tran Communications, Digital Signal Processing, Chinese Physics Letters, Chinese J of Electronics, Chinese J of Computer Science & Technology, Chinese J of Aeronautics, and so on. His research interests include complex systems theory and its applications to optimization and information sharing of the Internet, IoT and the so-called ubiquitous networks. FIRST QUARTER 2011

Jian Yuan received his Ph.D. degree in electrical engineering from the University of Electronic Science and Technology of China, in 1998. He is currently an associate professor in the Department of Electronic Engineering at Tsinghua University, Beijing, China. His main research interest is in complex dynamics of networked systems and dependability of mobile networks. Xiuming Shan received his B.S. degree in electronic engineering from Tsinghua University, Beijing, China, in 1970. He is the head and a chair professor of the Institute of High-speed Signal Processing and Network Transmission, Department of Electronic Engineering, Tsinghua University, Beijing, China. His research interest includes radar signal processing, computer networks, and complex systems. References [1] R. Pastor-Satorras and A. Vespignani, Evolution and Structure of the Internet: A Statistical Physics Approach. Cambridge, U.K.: Cambridge Univ. Press, 2004. [2] BitTorrent. (2003). Available: http://bitconjurer.org/ [3] Kazaa Media Desktop. (2001). Available: http://www.kazaa.com/

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