Patterns of link reciprocity in directed networks.

By Diego Garlaschelli, M. I. Loffredo. Physical Review Letters, 2004

439 citations recorded by the source corpus.

We address the problem of link reciprocity, the nonrandom presence of two mutual links between pairs of vertices. We propose a new measure of reciprocity that allows the ordering of networks according to their actual degree of correlation between mutual links. We find that real networks are always either correlated or anticorrelated, and that networks of the same type (economic, social, cellular, financial, ecological, etc.) display similar values of the reciprocity. The observed patterns are not reproduced by current models. This leads us to introduce a more general framework where mutual links occur with a conditional connection probability. In some of the studied networks we discuss the form of the conditional connection probability and the size dependence of the reciprocity.

Subfields: Management Science and Operations Research, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/cc0d3e12775c83747cafcbd5625809ae26bde6fa

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In Management Science and Operations Research

In Statistical and Nonlinear Physics

Citations in the corpus

Multirelational organization of large-scale social networks in an online world (2010, background): “Table 1 shows that networks with a positive connotation [friendship, private messages (PMs) and trades] are strongly reciprocal [31] (see [SI]), in the sense that node pairs have a high tendency to form bi-directional connections, while networks with a negative connotation (enmity, attack and bounty”
Comparison of online social relations in volume vs interaction: a case study of cyworld (2008, methodology): “We use Garlaschelli and Loffredo’s method to calculate the reciprocity coefficient ρ of the entire network based on link reciprocity [16].”
Growth of the flickr social network (2008, background): “Reciprocation has been proposed as an independent growth mechanism for large-scale directed graphs [6,22].”
Networks of Value Added Trade (2017, neutral): “…by providing new opportunities for developing countries to integrate into the world economy by joining a supply chain.10 8 Given that the networks of value-added trade have a time-varying density, panel (d) of Figure 1 presents the measure of reciprocity of Garlaschelli and Loffredo (2004b).”
Statistical mechanics of networks. (2004, background): “Behavior of this kind is seen, for example, in the world wide web, email networks, and neural and metabolic networks [33, 34, 35].”
The statistical physics of real-world networks (2018, methodology): “The typical null model used to study motifs in directed networks is obtained by constraining, in addition to degrees, also the number of reciprocal links per node [60–62], which is meaningful in many contexts.”
Synchronization in complex networks (2008, background): “Recent studies about the local organization of directed networks found that reciprocity (percentage of bi-directional links) in real networks differ clearly from models [160, 161], and suprisingly many real directed networks have very few short loops as compared to random networks [162].”
Toward link predictability of complex networks (2015, background): “…primary driving forces in network organization, including homophily (2 – 4), triadic closure (5 – 7), preferential attachment (8 – 10), reciprocity (11), and social balance (12), one or two of these mechanisms cannot provide a complete explanation; i.e., link formation in real-world networks is…”
Characterization of complex networks: A survey of measurements (2005, background): “n: = n↔ n . (58) The problem with this relation is that its value is only signiﬁcative with respect to a random version of the network, as it depends on the average degree. Garlaschelli and Loﬀredo [66] proposed the use of the correlation coeﬃcient of the adjacency matrix: ρ = P i6= j(aij − ¯a)(aji”
The evolution of the world trade web: a weighted-network analysis (2010, background): “Indeed, as found also by Serrano and Boguñá (2003) and Garlaschelli and Loffredo (2005), countries that hold more trade partners (high degree) are less clustered than those holding few partners.”
Statistical analysis of the social network and discussion threads in slashdot (2008, methodology): “Using the method proposed in [7], we quantify how the Slashdot network differs from a random network in the presence of two mutual links (edges in both directions) between pairs of nodes.”