A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the late 1960s. In the intervening years dozens of graph labelings techniques have been studied in over 1000 papers. Finding out what has been done for any particular kind of labeling and keeping up with new discoveries is difficult because of the sheer number of papers and because many of the papers have appeared in journals that are not widely available. In this survey I have collected everything I could find on graph labeling. For the convenience of the reader the survey includes a detailed table of contents and index.

/pdf/a-dynamic-survey-of-graph-labeling-198znmwxtq.pdf

A Dynamic Survey of Graph Labeling

Detecting anomalies in data is a vital task, with numerous high-impact applications in areas such as security, finance, health care, and law enforcement. While numerous techniques have been developed in past years for spotting outliers and anomalies in unstructured collections of multi-dimensional points, with graph data becoming ubiquitous, techniques for structured graph data have been of focus recently. As objects in graphs have long-range correlations, a suite of novel technology has been developed for anomaly detection in graph data. This survey aims to provide a general, comprehensive, and structured overview of the state-of-the-art methods for anomaly detection in data represented as graphs. As a key contribution, we give a general framework for the algorithms categorized under various settings: unsupervised versus (semi-)supervised approaches, for static versus dynamic graphs, for attributed versus plain graphs. We highlight the effectiveness, scalability, generality, and robustness aspects of the methods. What is more, we stress the importance of anomaly attribution and highlight the major techniques that facilitate digging out the root cause, or the `why', of the detected anomalies for further analysis and sense-making. Finally, we present several real-world applications of graph-based anomaly detection in diverse domains, including financial, auction, computer traffic, and social networks. We conclude our survey with a discussion on open theoretical and practical challenges in the field.

http://www3.cs.stonybrook.edu/~leman/pubs/14-dami-graphanomalysurvey.pdf

Graph based anomaly detection and description: a survey

In the statistics community, outlier detection for time series data has been studied for decades. Recently, with advances in hardware and software technology, there has been a large body of work on temporal outlier detection from a computational perspective within the computer science community. In particular, advances in hardware technology have enabled the availability of various forms of temporal data collection mechanisms, and advances in software technology have enabled a variety of data management mechanisms. This has fueled the growth of different kinds of data sets such as data streams, spatio-temporal data, distributed streams, temporal networks, and time series data, generated by a multitude of applications. There arises a need for an organized and detailed study of the work done in the area of outlier detection with respect to such temporal datasets. In this survey, we provide a comprehensive and structured overview of a large set of interesting outlier definitions for various forms of temporal data, novel techniques, and application scenarios in which specific definitions and techniques have been widely used.

https://romisatriawahono.net/lecture/rm/survey/machine%20learning/Gupta%20-%20Outlier%20Detection%20for%20Temporal%20Data%20-%202014.pdf

Outlier Detection for Temporal Data: A Survey

Detecting anomalies in data is a vital task, with numerous high-impact applications in areas such as security, finance, health care, and law enforcement. While numerous techniques have been developed in past years for spotting outliers and anomalies in unstructured collections of multi-dimensional points, with graph data becoming ubiquitous, techniques for structured {\em graph} data have been of focus recently. As objects in graphs have long-range correlations, a suite of novel technology has been developed for anomaly detection in graph data. 
This survey aims to provide a general, comprehensive, and structured overview of the state-of-the-art methods for anomaly detection in data represented as graphs. As a key contribution, we provide a comprehensive exploration of both data mining and machine learning algorithms for these {\em detection} tasks. we give a general framework for the algorithms categorized under various settings: unsupervised vs. (semi-)supervised approaches, for static vs. dynamic graphs, for attributed vs. plain graphs. We highlight the effectiveness, scalability, generality, and robustness aspects of the methods. What is more, we stress the importance of anomaly {\em attribution} and highlight the major techniques that facilitate digging out the root cause, or the `why', of the detected anomalies for further analysis and sense-making. Finally, we present several real-world applications of graph-based anomaly detection in diverse domains, including financial, auction, computer traffic, and social networks. We conclude our survey with a discussion on open theoretical and practical challenges in the field.

Graph-based Anomaly Detection and Description: A Survey

In recent years the use of graph based representation has gained popularity in pattern recognition and machine learning. As a matter of fact, object representation by means of graphs has a number of advantages over feature vectors. Therefore, various algorithms for graph based machine learning have been proposed in the literature. However, in contrast with the emerging interest in graph based representation, a lack of standardized graph data sets for benchmarking can be observed. Common practice is that researchers use their own data sets, and this behavior cumbers the objective evaluation of the proposed methods. In order to make the different approaches in graph based machine learning better comparable, the present paper aims at introducing a repository of graph data sets and corresponding benchmarks, covering a wide spectrum of different applications.

/pdf/iam-graph-database-repository-for-graph-based-pattern-3vjk9crz04.pdf

IAM Graph Database Repository for Graph Based Pattern Recognition and Machine Learning

Magic squares are among the more popular mathematical recreations. Over the last 50 years, many generalizations of magic ideas have been applied to graphs. Recently there has been a resurgence of interest in magic labelings due to a number of results that have applications to the problem of decomposing graphs into trees. Key features of this second edition include: a new chapter on magic labeling of directed graphs applications of theorems from graph theory and interesting counting arguments new research problems and exercises covering a range of difficulties a fully updated bibliography and index This concise, self-contained exposition is unique in its focus on the theory of magic graphs/labelings. It may serve as a graduate or advanced undergraduate text for courses in mathematics or computer science, and as reference for the researcher.

Magic Graphs

A vertex-magic total labeling of a graph with $v$ vertices and $e$ edges is defined as a one-to-one map taking the vertices and edges onto the integers $1, 2, . . . , v+e$ with the property that the sum of the label on a vertex and the labels on its incident edges is a constant independent of the choice of vertex.
Properties of these labelings are studied. It is shown how to construct labelings for several families of graphs, including cycles, paths, complete graphs of odd order and the complete bipartite graph $K_n,n$. It is also shown that labelings are impossible for some other classes of graphs.

Vertex-Magic Total Labelings of Graphs

In the management of large enterprise communication networks, it becomes difficult to detect and identify causes of abnormal change in traffic distributions when the underlying logical topology is ...

Detection of abnormal change in a time series of graphs

Intranets and Network Management.- Graph-Theoretic Concepts.- Event Detection Using Graph Distance.- Matching Graphs with Unique Node Labels.- Graph Similarity Measures for Abnormal Change Detection.- Median Graphs for Abnormal Change Detection.- Graph Clustering for Abnormal Change Detection.- Graph Distance Measures based on Intragraph Clustering and Cluster Distance.- Matching Sequences of Graphs.- Properties of the Underlying Graphs.- Distances, Clustering, and Small Worlds.- Tournament Scoring.- Prediction and Advanced Distance Measures.- Recovery of Missing Information in Graph Sequences.- Matching Hierarchical Graphs.

A Graph-Theoretic Approach to Enterprise Network Dynamics

An edge-magic total labeling on a graph G is a one-to-one map λ from $ V (G) \ cup E(G) $ onto the integers 1,2, …, v + e, where v = | V (G) | and e = | E(G) |, with the property that, given any edge xy, 

$$\lambda (x) + \lambda (xy) + \lambda (y) = k$$

for some constant k. In other words, wt(xy) = k for any choice of edge xy. Then k is called the magic sum of G. Any graph with an edge-magic total labeling will be called edge-magic. described.

/pdf/edge-magic-total-labelings-1rxa1mkr93.pdf

Walter D. Wallis

Papers

Magic Graphs

Vertex-Magic Total Labelings of Graphs

Detection of abnormal change in a time series of graphs

A Graph-Theoretic Approach to Enterprise Network Dynamics

Edge-Magic Total Labelings