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Mining interesting link formation rules in social networks
 In CIKM ’10
, 2010
"... Link structures are important patterns one looks out for when modeling and analyzing social networks. In this paper, we propose the task of mining interesting Link Formation rules (LFrules) containing link structures known as Link Formation patterns (LFpatterns). LFpatterns capture various dya ..."
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Link structures are important patterns one looks out for when modeling and analyzing social networks. In this paper, we propose the task of mining interesting Link Formation rules (LFrules) containing link structures known as Link Formation patterns (LFpatterns). LFpatterns capture various dyadic and/or triadic structures among groups of nodes, while LFrules capture the formation of a new link from a focal node to another node as a postcondition of existing connections between the two nodes. We devise a novel LFrule mining algorithm, known as LFRMiner, based on frequent subgraph mining for our task. In addition to using a supportconfidence framework for measuring the frequency and significance of LFrules, we introduce the notion of expected support to account for the extent to which LFrules exist in a social network by chance. Specifically, only LFrules with higherthanexpected support are considered interesting. We conduct empirical studies on two realworld social networks, namely Epinions and myGamma. We report interesting LFrules mined from the two networks, and compare our findings with earlier findings in social network analysis.
P.: The complexity of mining maximal frequent subgraphs
 In: Proceedings of the 32nd ACM SIGMODSIGACTSIGART Symposium on Principles of Database Systems, PODS 2013, ACM
, 2013
"... A frequent subgraph of a given collection of graphs is a graph that is isomorphic to a subgraph of at least as many graphs in the collection as a given threshold. Frequent subgraphs generalize frequent itemsets and arise in various contexts, from bioinformatics to the Web. Since the space of frequen ..."
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A frequent subgraph of a given collection of graphs is a graph that is isomorphic to a subgraph of at least as many graphs in the collection as a given threshold. Frequent subgraphs generalize frequent itemsets and arise in various contexts, from bioinformatics to the Web. Since the space of frequent subgraphs is typically extremely large, research in graph mining has focused on special types of frequent subgraphs that can be orders of magnitude smaller in number, yet encapsulate the space of all frequent subgraphs. Maximal frequent subgraphs (i.e., the ones not properly contained in any frequent subgraph) constitute the most useful such type. In this paper, we embark on a comprehensive investigation of the computational complexity of mining maximal frequent subgraphs. Our study is carried out by considering the effect of three different parameters: possible restrictions on the class of graphs; a fixed bound on the threshold; and a fixed bound on the number of desired answers. We focus on specific classes of connected graphs: general graphs, planar graphs, graphs of bounded degree, and graphs of bounded treewidth (trees being a special case). Moreover, each class has two variants: the one in which the nodes are unlabeled, and the one in which they are uniquely labeled. We delineate the complexity of the enumeration problem for each of these variants by determining when it is solvable in (total or incremental) polynomial time and when it is NPhard. Specifically, for the labeled classes, we show that bounding the threshold yields tractability but, in most cases, bounding the number of answers does not, unless P=NP; an exception is the case of labeled trees, where bounding either of these two parameters yields tractability. The state of affairs turns out to be quite different for the unlabeled classes. The main (and most challenging to prove) result concerns unlabeled trees: we show NPhardness, even if the input consists of two trees, and both the threshold and the number of desired answers are equal to just two. In other words, we establish that the following problem is NPcomplete: given two unlabeled trees, do they have more than one maximal subtree in common?
Efficient Counting of Network Motifs
"... Abstract—Counting network motifs has an important role in studying a wide range of complex networks. However, when the network size is large, as in the case of Internet Topology and WWW graphs counting the number of motifs becomes prohibitive. Devising efficient motif counting algorithms thus become ..."
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Abstract—Counting network motifs has an important role in studying a wide range of complex networks. However, when the network size is large, as in the case of Internet Topology and WWW graphs counting the number of motifs becomes prohibitive. Devising efficient motif counting algorithms thus becomes an important goal. In this paper, we present efficient counting algorithms for 4node motifs. We show how to efficiently count the total number of each type of motif, and the number of motifs adjacent to a node. We further present a new algorithm for node positionaware motif counting, namely partitioning the motif count by the node position in the motif. Since our algorithm is based on motifs, which are noninduced we also show how to calculate the count of induced motifs given the noninduced motif count. Finally, we report on initial implementation performance result using evaluation on a largescale graph. A. Motif Discovery I.
Characteristics of Small Social Networks
, 2010
"... Two dozen networks are analyzed using three parameters that attempt to capture important properties of social networks: leadership L, member bonding B, and diversity of expertise D. The first two of these parameters have antecedents, the third is new. A key part of the analysis is to examine network ..."
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Two dozen networks are analyzed using three parameters that attempt to capture important properties of social networks: leadership L, member bonding B, and diversity of expertise D. The first two of these parameters have antecedents, the third is new. A key part of the analysis is to examine networks at multiple scales by dissecting the entire network into its n subgraphs of a given radius of two edge steps about each of the n nodes. This scalebased analysis reveals constraints on what we have dubbed “cognitive” networks, as contrasted with biological or physical networks. Specifically, “cognitive” networks appear to maximize bonding and diversity over a range of leadership dominance. Asymptotic relations between the bonding and diversity measures are also found when small, nearly complete subgraphs are aggregated to form larger networks. This aggregation probably underlies changes in a regularity among the LBD parameters; this regularity is a Ushaped function of networks size, n, which is minimal for networks around 80 or so nodes. 1.0 Overview
Social Networks
"... Link structures are important patterns one looks out for when modeling and analyzing social networks. In this paper, we propose the task of mining interesting Link Formation rules (LFrules) containing link structures known as Link Formation patterns (LFpatterns). LFpatterns capture various dyadic ..."
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Link structures are important patterns one looks out for when modeling and analyzing social networks. In this paper, we propose the task of mining interesting Link Formation rules (LFrules) containing link structures known as Link Formation patterns (LFpatterns). LFpatterns capture various dyadic and/or triadic structures among groups of nodes, while LFrules capture the formation of a new link from a focal node to another node as a postcondition of existing connections between the two nodes. We devise a novel LFrule mining algorithm, known as LFRMiner, based on frequent subgraph mining for our task. In addition to using a supportconfidence framework for measuring the frequency and significance of LFrules, we introduce the notion of expected support to account for the extent to which LFrules
Proceedings of the Fourth International AAAI Conference on Weblogs and Social Media To Be a Star Is Not Only Metaphoric: From Popularity to Social Linkage
"... The emergence of online platforms allowing to mix self publishing activities and social networking offers new possibilities for building online reputation and visibility. In this paper we present a method to analyze the online popularity that takes into consideration both the success of the publishe ..."
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The emergence of online platforms allowing to mix self publishing activities and social networking offers new possibilities for building online reputation and visibility. In this paper we present a method to analyze the online popularity that takes into consideration both the success of the published content and the social network topology. First, we adapt the Kohonen self organizing maps in order to cluster the users of online platforms depending on their audience and authority characteristics. Then, we perform a detailed analysis of the manner nodes are organized in the social network. Finally, we study the relationship between the network local structure around each node and the corresponding user’s popularity. We apply this method to the MySpace music social network. We observe that the most popular artists are centers of star shaped social structures and that it exists a fraction of artists who are involved in community and social activity dynamics independently of their popularity. This method based on a learning algorithm and on network analysis appears to be a robust and intuitive technique for a rich description of the online behavior. 1.