Link prediction for tree-like networks

Abstract

Link prediction is the problem of predicting the location of either unknown or fake links from uncertain structural information of a network. Link prediction algorithms are useful in gaining insight into different network structures from partial observations of exemplars. However, existing link prediction algorithms only focus on regular complex networks and are overly dependent on either the closed triangular structure of networks or the so-called preferential attachment phenomenon. The performance of these algorithms on highly sparse or treelike networks is poor. In this letter, we proposed a method that is based on the network heterogeneity. We test our algorithms for three real large sparse networks: a metropolitan water distribution network, a Twitter network, and a sexual contact network. We find that our method is effective and performs better than traditional algorithms, especially for the Twitter network. We further argue that heterogeneity is the most obvious defining pattern for complex networks, while other statistical properties failed to be predicted. Moreover, preferential attachment based link prediction performed poorly and hence we infer that preferential attachment is not a plausible model for the genesis of many networks. We also suggest that heterogeneity is an important mechanism for online information propagation.

Growing networks with communities: A distributive link model

“…In what follows, we show network structures that are constructed via our model and their degree distributions. In regular networks (networks with many crossing links 16 ), with the increasing probability of the appearance of new communities, the degree of the hub node decreases-consistent with the hypothesis of our model. Surprisingly, our model can also construct a tree-like network with natural increasing new branches (communities).…”

“…Next, we set m = 1 and p = 1 and then directly construct a tree-like network. 16 As shown in Fig. 3, the surprising result is that our model is very similar to a naturally evolving tree.…”

“…In particular, the degree distribution of growing engineering networks is usually influenced by both geography and resource-driven demand; hence, links cannot be predicted well via an algorithm that is based solely on the principle of pure preferential attachment. 15,16 On the other hand, communities appear in many complex networks and are frequently associated with important functions of those networks. [17][18][19][20] Research into community detection also has recently attracted increasing attention.…”

“…Many real-world systems are naturally represented as tree-like networks with almost no closed triangular structure. 16 Here, we set k, m, p, and n as shown in Fig. 3.…”

A novel metric for community detection

“…In this paper we focus on the fact that links within a community are more predictable than external links (Yan and Gregory 2012;Cannistraci, Alanis-Lobato, and Ravasi 2013;Ding et al 2016) -due simply to the assumption that relationships within a real community are stronger (and perhaps more structured) than the external relationships. Hence, we adopt ideas from link prediction theory -where links can be predicted based on statistical characterisation of network structure (Liben-Nowell and Kleinberg 2007;Redner 2008;Lü et al 2015;Shang et al 2019) -to measure the predictability of network substructure. We propose a new metric for community detection which is based on the principle that links within a community should achieve a higher link prediction performance than external links (Yan and Gregory 2012;Cannistraci, Alanis-Lobato, and Ravasi 2013;Ding et al 2016).…”