Prediction of Arrival of Nodes in a Scale Free Network

Abstract

Most of the networks observed in real life obey power-law degree distribution. It is hypothesized that the emergence of such a degree distribution is due to preferential attachment of the nodes. Barabasi-Albert model is a generative procedure that uses preferential attachment based on degree and one can use this model to generate networks with power-law degree distribution. In this model, the network is assumed to grow one node every time step. After the evolution of such a network, it is impossible for one to predict the exact order of node arrivals. We present in this article, a novel strategy to partially predict the order of node arrivals in such an evolved network. We show that our proposed method outperforms other centrality measure based approaches. We bin the nodes and predict the order of node arrivals between the bins with an accuracy of above 80%.

Phase Transition in the Recoverability of Network History

“…Less obvious is the fact that a second body of work, rooted in information theory and computer science, also makes the statement that growth processes can generate the history of real complex networks. This second strand of literature [29][30][31][32][33][34][35][36] focuses on temporal reconstruction problems on treelike networks generated by random attachment processes [6,37]. It has led to efficient root-finding algorithms (whose goal is to find the first node) [29][30][31][32], and to approximative reconstruction algorithms on trees [33][34][35].…”

“…This second strand of literature [29][30][31][32][33][34][35][36] focuses on temporal reconstruction problems on treelike networks generated by random attachment processes [6,37]. It has led to efficient root-finding algorithms (whose goal is to find the first node) [29][30][31][32], and to approximative reconstruction algorithms on trees [33][34][35]. Applying any of these algorithms to a real network amounts to assuming that growth processes-here random attachment models-are likely generative models.…”

Learning and benefiting from structured correlations

“…Since real world networks are unlabelled with respect to time, a natural problem to consider on such networks is the arrival order inference problem. That is, given a snapshot in time of the network, identify the order in which nodes join the network [108].…”

“…As an example for why the linkage information is also necessary, consider a situation where the last two nodes to arrive connect to disjoint subsets of the nodes, then by swapping their neighborhoods we create the same graph with the same arrival order but this is a different run of the underlying stochastic process. [108] consider only the arrival order but we will consider a run of the process to consist of both the arrival order as well as the linkage information. Henceforth we will use the term arrival order to include the associated linkage information as well.…”

“…By sampling uniformly one can use the majority vote among a set of samples to decide which came earlier and further using [97] one can even approximate the probability that the one vertex came before the other. Such questions were heuristically addressed in [108].…”