Temporal Network Motifs: Models, Limitations, Evaluation

  title={Temporal Network Motifs: Models, Limitations, Evaluation},
  author={Penghang Liu and Valerio Guarrasi and Ahmet Erdem Sariy{\"u}ce},
Investigating the frequency and distribution of small subgraphs with a few nodes/edges, i.e., motifs, is an effective analysis method for static networks. Motif-driven analysis is also useful for temporal networks where the number of motifs is significantly larger due to the additional temporal information on edges. This variety makes it challenging to design a temporal motif model that can consider all aspects of temporality. In the literature, previous works have introduced various models… 
Scalable Motif Counting for Large-scale Temporal Graphs
A hierarchical parallel framework that featuring both inter- and intra-node parallel strategies, and fully leverages the multi-threading capacity of modern CPU to concurrently count all temporal motifs in large-scale temporal graphs is proposed.
Analytical Models for Motifs in Temporal Networks
This work develops the Temporal Activity State Block Model, a fast and accurate model-based method for counting motifs in temporal networks, and develops an efficient model fitting method, so that for a given network, it quickly fit the TASMB model and compute motif frequencies.
Quantifying Uncertainty for Temporal Motif Estimation in Graph Streams under Sampling
The consistency and the asymptotic normality of a certain Horvitz-Thompson type of estimator is established in an edge sampling framework for deterministic graph streams, which can be used to construct confidence intervals and conduct hypothesis testing for the temporal motif count under sampling.
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A new algorithm, DOTTT (Degeneracy Oriented Temporal Triangle Totaler), that exactly counts all directed variants of (δ1,3, δ2,3), and it is proved that DOTTT runs in O(mκłog m) time, where m is the number of (temporal) edges and κ is the graph degeneracy (max core number).
PRESTO: Simple and Scalable Sampling Techniques for the Rigorous Approximation of Temporal Motif Counts
This work presents an efficient and scalable algorithm, based on a simple but effective sampling approach, which renders the algorithm practical for very large datasets, and provides estimates of temporal motif counts which are more accurate than the state-of-the-art sampling algorithms, with significantly lower running time than exact approaches.
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Algorithms and code are presented to model graph evolution in terms of collections of Subgraph-to-Subgraph Transitions, and the SST framework is used to create link prediction models which produce highly interpretable results.


Motifs in Temporal Networks
A notion of a temporal network motif as an elementary unit of temporal networks is developed and a general methodology for counting such motifs is provided and it is found that measuring motif counts at various time scales reveals different behavior.
Event Pattern Matching over Graph Streams
The semantics and efficient online algorithms for this important and intriguing problem of event pattern matching are studied, and approaches are evaluated with extensive experiments over real world datasets in four different domains.
Exploring the structure and function of temporal networks with dynamic graphlets
When the ability of the new approach to characterize the structure and function of an entire temporal network or of individual nodes is evaluated, it is found that the dynamic graphlet approach outperforms the staticgraphlet approach, which indicates that accounting for temporal information helps.
Network motifs: simple building blocks of complex networks.
Network motifs, patterns of interconnections occurring in complex networks at numbers that are significantly higher than those in randomized networks, are defined and may define universal classes of networks.
Temporal motifs in time-dependent networks
The framework of temporal motifs is introduced to study the mesoscale topological–temporal structure of temporal networks in which the events of nodes do not overlap in time and a mapping from event sequences to coloured directed graphs is provided that enables an efficient algorithm for identifying temporal motifS.
SNAP Datasets
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  • 2014
Interaction data from the Copenhagen Networks Study
This work describes the multi-layer temporal network which connects a population of more than 700 university students over a period of four weeks, and expects that reuse of this dataset will allow researchers to make progress on the analysis and modeling of human social networks.
New Algorithms for Counting Temporal Graph Pattern
An exact algorithm based on the time first search (TFS) algorithm can reduce the intermediate results generated in the graph isomorphism and has high computational efficiency and an estimation algorithm can greatly reduce the running time while guaranteeing the accuracy.
TM-Miner: TFS-Based Algorithm for Mining Temporal Motifs in Large Temporal Network
This paper defines the temporal motif as a frequently connected subgraph that has a similar sequence of information flows and proposes an efficient algorithm called TM-Miner, which builds a canonical labeling system that uses a new lexicographic order and maps the temporal graph to the unique minimum TFS code.
A Guide to Temporal Networks