Relay-Linking Models for Prominence and Obsolescence in Evolving Networks

Abstract

The rate at which nodes in evolving social networks acquire links (friends, citations) shows complex temporal dynamics. Preferential attachment and link copying models, while enabling elegant analysis, only capture rich-gets-richer e ects, not aging and decline. Recent aging models are complex and heavily parameterized; most involve estimating 1-3 parameters per node. These parameters are intrinsic: they explain decline in terms of events in the past of the same node, and do not explain, using the network, where the linking attention might go instead. We argue that traditional characterization of linking dynamics are insu cient to judge the faithfulness of models. We propose a new temporal sketch of an evolving graph, and introduce several new characterizations of a network's temporal dynamics. Then we propose a new family of frugal aging models with no per-node parameters and only two global parameters. Our model is based on a surprising inversion or undoing of triangle completion, where an old node relays a citation to a younger follower in its immediate vicinity. Despite very few parameters, the new family of models shows remarkably better t with real data. Before concluding, we analyze temporal signatures for various research communities yielding further insights into their comparative dynamics. To facilitate reproducible research, we shall soon make all the codes and the processed dataset available in the public domain.

Analysis of reference and citation copying in evolving bibliographic networks

“…Fitness parameters, modeling a node's competitiveness to attract links, add another dimension to complex growth models [2,22]. Singh et al [21] propose an aging model where new node v tentatively chooses a base node u, but then cites a node x that cites u, in case u is "too old".…”

“…In this paper, we present a new citation network growth model and call it RefOrCite. Like FF and RelayCite [21], RefOrCite is based on reallife scholarly explorations in citation networks. To trace the origins of an idea, we need to explore back in time, following outlinks.…”

“…It helps us derive mean-field estimates for degree distribution, triangle count and some other properties. We present two variants of RefOrCite: RefOrCite1, where, after linking v to u, we walk only to newer nodes x that link to u (as in RelayCite [21]); and RefOrCite2, in which, like FF, walking to both in-and out-links of u is allowed. Accordingly, RefOrCite is characterized by one or two parameters.…”

“…In RefOrCite, a new node j appears at time t + 1 and selects an older 'base' node i uniformly randomly from G t , where G t is the network at time t and G t+1 = {j} ∪ G t . The base node is not sampled preferentially: that would increase the selection of older nodes beyond what is warranted by obsolescence models [21]. Uniform base node sampling also leads to heavy-tailed degrees and other realistic properties.…”

“…We review a series of standard properties and corresponding modeling approaches in the rest of this section: tail-heavy degree distribution, plentiful bipartite cores and triangles, densification and reduction of diameter as time passes, and the effects of obsolescence of nodes. In Section 2, we propose RefOrCite, a variation based on the Forest Fire (FF) [15] and the RelayCite [21] models. The key idea in all three models is that new nodes choose and link to a 'base' node, and then nodes in its neighborhood.…”