KWIQ: Answering k-core Window Queries in Temporal Networks

Abstract

Understanding the evolution of communities and the factors that contribute to their development, stability and disappearance over time is a fundamental problem in the study of temporal networks. The concept of 𝑘 -core is one of the most popular metrics to detect communities. Since the 𝑘 -core of a temporal network changes with time, an important question arises: Are there nodes that always remain within the 𝑘 -core? In this paper, we explore this question by introducing the notion of core-invariant nodes . Given a temporal window ∆ and a parameter K , the core-invariant nodes are those that are part of the K -core throughout ∆. Core-invariant nodes have been shown to dictate the stability of networks, while being also useful in detecting anomalous behavior. The complexity of finding core-invariant nodes is 𝑂 ( | ∆ |×| 𝐸 | ), which is exorbitantly high for million-scale networks. We overcome this computational bottleneck by designing an algorithm called Kwiq. Kwiq efficiently processes the cascading impact of network updates through a novel data structure called orientation graph. Through extensive experiments on real temporal networks containing millions of nodes, we establish that the proposed pruning strategies are more than 5 times faster than baseline strategies.