Abstract
Temporal networks are graphs where each edge is associated with a timestamp denoting when two nodes interact. Temporal Subgraph Isomorphism (TSI) aims at retrieving all the subgraphs of a temporal network (called target) matching a smaller temporal network (called query), such that matched target edges appear in the same chronological order of corresponding query edges. Few algorithms have been proposed to solve the TSI problem (or variants of it) and most of them are applicable only to small or specific queries. In this paper we present TemporalRI, a new subgraph isomorphism algorithm for temporal networks with multiple contacts between nodes, which is inspired by RI algorithm. TemporalRI introduces the notion of temporal flows and uses them to filter the search space of candidate nodes for the matching. Our algorithm can handle queries of any size and any topology. Experiments on real networks of different sizes show that TemporalRI is very efficient compared to the state-of-the-art, especially for large queries and targets.
Highlights
Introduction and related worksGraphs are mathematical objects that are suitable to represent complex systems formed by a set of entities that interact each other
For the comparison with other tools, we only focused on exact motifs counting or subgraph isomorphism algorithms having the same or very similar definition of temporal queries (Mackey et al 2018; Sun et al 2019b; Paranjape et al 2017)
The speedup is higher for larger queries and denser networks. We believe that this is due to two aspects that distinguish TemporalRI from Mackey’s algorithm: (1) the effective filtering of candidates done using temporal flows, (2) the ordering of query edges based on the degrees of query nodes
Summary
Graphs (or networks) are mathematical objects that are suitable to represent complex systems formed by a set of entities that interact each other. Entities are called nodes while their interactions are called edges. In many applications graphs are considered as static objects, without taking into account when or how long two nodes interact. Complex systems are inherently dynamic and evolve during time. In a remote communication system, users may enter the network anytime to start communications with other users. In a protein-protein interaction network a protein can establish temporary interactions with one or more proteins to perform a biological process or transmit a signal to a cell. Time is crucial to understand the formation and the evolution of such systems. By associating a time information to each edge, a network becomes temporal
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