Graph Exploration Research Articles

Exemplar-based Layout Fine-tuning for Node-link Diagrams.

We design and evaluate a novel layout fine-tuning technique for node-link diagrams that facilitates exemplar-based adjustment of a group of substructures in batching mode. The key idea is to transfer user modifications on a local substructure to other substructures in the entire graph that are topologically similar to the exemplar. We first precompute a canonical representation for each substructure with node embedding techniques and then use it for on-the-fly substructure retrieval. We design and develop a light-weight interactive system to enable intuitive adjustment, modification transfer, and visual graph exploration. We also report some results of quantitative comparisons, three case studies, and a within-participant user study.

RapidMatch

A subgraph query searches for all embeddings in a data graph that are identical to a query graph. Two kinds of algorithms, either graph exploration based or join based, have been developed for processing subgraph queries. Due to algorithmic and implementational differences, join-based systems can handle query graphs of a few vertices efficiently whereas exploration-based approaches typically process up to several tens of vertices in the query graph. In this paper, we first compare these two kinds of methods and prove that the complexity of result enumeration in state-of-the-art exploration-based methods matches that of the worst-case optimal join. Furthermore, we propose RapidMatch, a holistic subgraph query processing framework integrating the two approaches. Specifically, RapidMatch not only runs relational operators such as selections and joins, but also utilizes graph structural information, as in graph exploration, for filtering and join plan generation. Consequently, it outperforms the state of the art in both approaches on a wide range of query workloads.

TS-Extractor: large graph exploration via subgraph extraction based on topological and semantic information.

Exploring large graphs is difficult due to their large size and semantic information such as node attributes. Extracting only a subgraph relevant to the user-specified nodes (called focus nodes) is an effective strategy for exploring a large graph. However, existing approaches following this strategy mainly focus on graph topology and do not fully consider node attributes, resulting in the lack of clear semantics in the extracted subgraphs. In this paper, we propose a novel approach called TS-Extractor that can extract a relevant subgraph around the user-selected focus nodes to help the user explore the large graph from a local perspective. By combining the graph topology and the user-selected node attributes, TS-Extractor can extract and visualize a connected subgraph that contains as many nodes sharing the same/similar attribute values with the focus nodes as possible, thereby providing the user with clear semantics. Based on TS-Extractor, we develop a Web-based graph exploration system that allows users to interactively extract, analyze and expand subgraphs. Through two case studies and a user study, we demonstrate the usability and effectiveness of TS-Extractor.Graphic abstract

Knowledge graph exploration

Knowledge graphs (KGs) represent facts in the form of subject-predicate-object triples and are widely used to represent and share knowledge on the Web. Their ability to represent data in complex domains augmented with semantic annotations has attracted the attention of both research and industry. Yet, their widespread adoption in various domains and their generation processes have made the contents of these resources complicated. We speak of knowledge graph exploration as of the gradual discovery and understanding of the contents of a large and unfamiliar KG. In this paper, we present an overview of the state-of-the-art approaches for KG exploration. We divide them into three areas: profiling, search, and analysis and we argue that, while KG profiling and KG exploratory search received considerable attention, exploratory KG analytics is still in its infancy. We conclude with an overview of promising future research directions towards the design of more advanced KG exploration techniques.

Laminations of a graph on a pair of pants

A lamination of a graph embedded on a surface is a collection of pairwise disjoint non-contractible simple closed curves drawn on the graph. In the case when the surface is a sphere with three punctures (a.k.a. a pair of pants), we first identify the lamination space of a graph embedded on that surface as a lattice polytope, then we characterize the polytopes that arise as the lamination space of some graph on a pair of pants. This characterizes the image of a simplified variant of the spectral map for the vector bundle Laplacian for a flat connection on a pair of pants. The proof uses a graph exploration technique akin to the peeling of planar maps.

Generalizing Multi-agent Graph Exploration Techniques

The system of multiple agents working in coordination for a given task has several advantages on faster completion, fault-tolerance, etc. To develop a multi-agent graph exploration technique, the following are defined: 1) the way agents communicate, 2) initial placement of agents and 3) the role of each agent in a systematic search of (unexplored) vertices/edges in the graph. However, the general concepts and requirements are not developed. Hence, we attempt to generalize the multi-agent system for graph exploration. The graph may or may not be known a priori. The proposed representation for the multi-agent system is aimed to provide general conditions for declaring completion and finite time completion applicable to any multi-agent system for graph exploration. Results are proved using linear algebraic concepts on graphs. We also propose modifications in the incidence matrix as a data structure for organized information exchange between the agents. Further, a generic algorithm for the system of multiple agents exploring a graph is developed. The algorithm is based on the proposed generalized framework and modified incidence matrix. Simulation videos show the applicability of proposed generalization in exploring a graph using multiple agents for various combinations of initial placements of agents, search strategy, and interagent communication method. Further, We use the generalization to show the application of the proposed method in multi-robot exploration and map building of an unknown environment represented by a graph.

Online graph exploration on a restricted graph class: Optimal solutions for tadpole graphs

We study the problem of online graph exploration on undirected graphs, where a searcher has to visit every vertex and return to the origin. Once a new vertex is visited, the searcher learns of all neighboring vertices and the connecting edge weights. The goal of such an exploration is to minimize its total cost, where each edge traversal incurs a cost of the corresponding edge weight.We investigate the problem on tadpole graphs (also known as dragons, kites), which consist of a cycle with an attached path. The construction by Miyazaki et al. (The online graph exploration problem on restricted graphs, IEICE Transactions 92-D (9), 2009) can be extended to show that every online algorithm on these graphs must have a competitive ratio of 2−ε, but the authors did not investigate non-unit edge weights. We show via amortized analysis that a greedy approach yields a matching competitive ratio of 2 on tadpole graphs, for arbitrary non-negative edge weights. Moreover, we also briefly discuss the topic of advice complexity on cycle and tadpole graphs.

Interactive exploration of large time-dependent bipartite graphs

Abstract Bipartite graphs are typically visualized using linked lists or matrices, but these visualizations neither scale well nor do they convey temporal development. We present a new interactive exploration interface for large, time-dependent bipartite graphs. We use two clustering techniques to build a hierarchical aggregation supporting different exploration strategies. Aggregated nodes and edges are visualized as linked lists with nested time series. We demonstrate two use cases: finding advertising expenses of public authorities following similar temporal patterns and comparing author-keyword co-occurrences across time. Through a user study, we show that linked lists with hierarchical aggregation lead to more insights than without.

On the minimal diameter of closed hyperbolic surfaces

We prove that the minimal diameter of a closed orientable hyperbolic surface of genus g is asymptotic to log g as g → ∞ . The proof relies on a random construction, which we analyze using lattice-point counting theory and the exploration of random trivalent graphs.

Combining Graph Exploration and Fragmentation for Scalable RDF Query Processing

The flexibility offered by the Resource Description Framework (RDF) has led it to become a very popular standard for representing data with an undefined or variable schema using the concept of triples. Its success has resulted in many large scale multidisciplinary datasets, that have prompted the development of efficient RDF processing systems. Current approaches can be distinguished into two groups: the first, adopting the relational model storing the triples in tables, and the second creating data structures that model RDF data as a graph. The strategies of the first group are more easily scalable since they apply optimization strategies from the relational model like indexing and fragmentation. However, these approaches suffer many overheads when dealing with complex queries (e.g. compounded SPARQL graphs involving filters) persistent in existing applications. On the other hand, graph-based systems that use more complex data structures fail to efficiently manage the main memory and are not scalable in computer hardware with limited resources. In this paper, we propose a novel approach to perform queries (Basic Graph Patterns, Wildcards, Aggregations and Sorting) on RDF data. We propose to combine both RDF graph exploration with physical fragmentation of triples. In this work, we describe our graph-based storage and query evaluation models. Then, we detail the architecture of our system and we largely explain the strategy, based in the Volcano execution model, used to manage the main memory at query runtime. We conducted extensive experiments on synthetic and real datasets to evaluate the efficiency of our proposal. We compared our performance with a relational-based (Virtuoso), a graph-based (gStore) and an intensive-indexing (RDF-3X) approach. According to our evaluation, our system offers the best compromise between efficient query processing and scalability.

Using knowledge anchors to facilitate user exploration of data graphs

This paper investigates how to facilitate users’ exploration through data graphs. The prime focus is on knowledge utility, i.e. increasing a user’s domain knowledge while exploring a data graph, which is crucial in the vast number of user-facing semantic web applications where the users are not experts in the domain. We introduce a highly unique exploration support mechanism underpinned by the subsumption theory for meaningful learning. A core algorithmic component for operationalising the subsumption theory for meaningful learning is the automatic identification of knowledge anchors in a data graph (KADG). We present several metrics for identifying KADG which are evaluated against familiar concepts in human cognitive structures. The second key component is a subsumption algorithm that utilises KADG for generating exploration paths for knowledge expansion. The implementation of the algorithm is applied in the context of a Semantic data browser in a music domain. The resultant exploration paths are evaluated in a task-driven experimental user study compared to free data graph exploration. The findings show that exploration paths, based on subsumption and using knowledge anchors, lead to significantly higher increase in the users’ conceptual knowledge and better usability than free exploration of data graphs. The work opens a new avenue in semantic data exploration which investigates the link between learning and knowledge exploration. We provide the first framework that adopts educational theories to inform data graph exploration for knowledge expansion which extends the value of exploration and enables broader applications of data graphs in systems where the end users are not experts in the specific domain.

IMPROVING RELIABILITY IN MAS BY RULE BASED LOGIC AND CRYPTOGRAPHIC TECHNIQUES

Mobile agent (MA) is a composition of software paradigm, having the capability to move from one host to another across dynamic network environment and execute task assigned by its user. Reliability is one of the most important issues in mobile agent-based system (MAS) which was addressed by many researchers. In this paper, we enhance the reliability in MAS with the support of intrusion detection system (IDS) and effective routing. Routing is an important process to find optimal path which improves network throughput and reliability. Collision-free (CF) – network graph exploration method is designed for identifying optimal path for MAs. Security is a crucial aspect due to various malicious node activities and must be considered while estimating reliability. In our process, HMAC-SHA1 algorithm is performed for detecting malicious agent and rule-based logic (RBL) is designed to identify malicious host. Further, we calculate reliability of MAS with respect to status of network and its condition which includes link connectivity and malicious node probability. Finally, we are simulating our performance by using various factors such as size of MAS, malicious ratio and number of mobile agents in MAS, etc. These factors are significant to show improved reliability of our proposed system.

Collectives of automata on infinite grid graph with deterministic vertex labeling

Automata walking on graphs are a mathematical formalization of autonomous mobile agents with limited memory operating in discrete environments. Under this model broad area of studies of the behaviour of automata in finite and infinite labyrinths (a labyrinth is an embedded directed graph of special form) arose and intensively developing. Research in this regard received a wide range of applications, for example, in the problems of image analysis and navigation of mobile robots. Automata operating in labyrinths can distinguish directions, that is, they have a compass. This paper examines vertex labellings of infinite square grid graph thanks to these labellings a finite automaton without a compass can walk along graph in any arbitrary direction. The automaton looking over neighbourhood of the current vertex and may move to some neighbouring vertex selected by its label. We propose a minimal deterministic traversable vertex labelling that satisfies the required property. A labelling is said to be deterministic if all vertices in closed neighbourhood of every vertex have different labels. It is shown that minimal deterministic traversable vertex labelling of square grid graph uses labels of five different types. Minimal deterministic traversable labelling of subgraphs of infinite square grid graph whose degrees are less than four are developed. The key problem for automata and labyrinths is the problem of constructing a finite automaton that traverse a given class of labyrinths. We say that automaton traverse infinite graph if it visits any randomly selected vertex of this graph in a finite time. It is proved that a collective of one automaton and three pebbles can traverse infinite square grid graph with deterministic labelling and any collective with fewer pebbles cannot. We consider pebbles as automata of the simplest form, whose positions are completely determined by the remaining automata of the collective. The results regarding to exploration of an infinite deterministic square grid graph coincide with the results of A.V. Andzhan (Andzans) regarding to traversal of an infinite mosaic labyrinth without holes. It follows from above that infinite grid graph after constructing a minimal traversable deterministic labelling on it and fixing two pairs of opposite directions on it becomes an analogue of an infinite mosaic labyrinth without holes.

Exploring knowledge graphs for the identification of concept prerequisites

Learning basic concepts before complex ones is a natural form of learning. Automated systems and instructional designers evaluate and order concepts’ complexity to successfully generate and recommend or adapt learning paths. This paper addresses the specific challenge of accurately and adequately identifying concept prerequisites using semantic web technologies for a basic understanding of a particular concept within the context of learning: given a target concept c, the goals are to (a) find candidate concepts that serve as possible prerequisite for c; and, (b) evaluate the prerequisite relation between the target and candidates concepts via a supervised learning model. Our four step approach consists of (i) an exploration of Knowledge Graphs in order to identify possible candidate concepts; (ii) the creation of a set of potential concepts; (iii) deployment of supervised learning model to evaluate a proposed list of prerequisite relationships regarding the target set; and, (iv) validation of our approaching using a ground truth of 80 concepts from different domains (with a precision varying between 76% and 96%).

BOTS AMONG US: PREVALENCE, INFLUENCE, AND ROLES OF AUTOMATED ACCOUNTS IN THE GERMAN TWITTER FOLLOW NETWORK

Social bots are undermining trust in social media. They spread low-credibility content, fake news, and spam. However, most research is based on bots that actively share links or keywords, rather than assessing the longer-term presence of bots as an integral part of platforms. To address this gap, we present what to our knowledge is the first study that assesses the prevalence, influence, and roles of automated accounts in a Twitter follow network on a national scale. This allows us to analyse the potential impact of bots beyond the context of single events and topics.
 To collect a follow network of the most central accounts in the German-speaking Twittersphere, we have adapted the rank-degree method, a graph exploration method that is able to identify the most influential spreaders within complex networks, as a data mining method using the cost-free standard Twitter API. To identify bots, we employ the Botometer API. Both methods combined allow us to localise bots within topical clusters, to estimate their potential influence, and to assess the roles of the most central bots.
 Our findings indicate that bots have only a low negative impact on the German-speaking Twittersphere. However, the most sophisticated bots will likely remain absent from our study, as false negatives. Similarly, trolls and semi-automated accounts necessitate further research. Our new sampling approach combined with Botometer is promising, for example, for Twitterspheres based on other languages. The study itself opens further avenues of enquiry, such as a long-term monitoring of automated accounts in the German Twittersphere.

Eigenedge: A measure of edge centrality for big graph exploration

Abstract As we are in the age of big data, graph data become bigger. A big graph normally has an overwhelming number of edges. Existing metrics of edge centrality are not quite suitable for dealing with such a large graph. A novel metric for measuring the importance of edges in a graph is introduced in this paper. Compared with the other six popular matrices with respect to a number of real-world graphs, the proposed metric is capable of capturing the structural feature of a graph in a scalable way. The comprehensive experiments have demonstrated the performance of the proposed metric. According to this metric, a filtering approach is presented to reduce the visual clutter of a layout in a way that the hidden patterns can be revealed gradually. As evidenced by real-world examples, our approach allows users to explore graphs in real-time with a high level of details in an interactive way in order to gain insight into graph data.

Tight Bounds for Undirected Graph Exploration with Pebbles and Multiple Agents

We study the problem of deterministically exploring an undirected and initially unknown graph with n vertices either by a single agent equipped with a set of pebbles or by a set of collaborating agents. The vertices of the graph are unlabeled and cannot be distinguished by the agents, but the edges incident to a vertex have locally distinct labels. The graph is explored when all vertices have been visited by at least one agent. In this setting, it is known that for a single agent without pebbles Θ(log n ) bits of memory are necessary and sufficient to explore any graph with at most n vertices. We are interested in how the memory requirement decreases as the agent may mark vertices by dropping and retrieving distinguishable pebbles or when multiple agents jointly explore the graph. We give tight results for both questions showing that for a single agent with constant memory Θ(log log n ) pebbles are necessary and sufficient for exploration. We further prove that using collaborating agents instead of pebbles does not help as Θ(log log n ) agents with constant memory each are necessary and sufficient for exploration. For the upper bounds, we devise an algorithm for a single agent with constant memory that explores any n -vertex graph using O (log log n ) pebbles, even when n is not known a priori . The algorithm terminates after polynomial time and returns to the starting vertex. We further show that the algorithm can be realized with additional constant-memory agents rather than pebbles, implying that O (log log n ) agents with constant memory can explore any n -vertex graph. For the lower bound, we show that the number of agents needed for exploring any graph with at most n vertices is already Ω(log log n ) when we allow each agent to have at most O ((log n ) 1 -ε) bits of memory for any ε > 0. Our argument also implies that a single agent with sublogarithmic memory needs Θ(log log n ) pebbles to explore any n -vertex graph.

ROBOKOP: an abstraction layer and user interface for knowledge graphs to support question answering.

SummaryKnowledge graphs (KGs) are quickly becoming a common-place tool for storing relationships between entities from which higher-level reasoning can be conducted. KGs are typically stored in a graph-database format, and graph-database queries can be used to answer questions of interest that have been posed by users such as biomedical researchers. For simple queries, the inclusion of direct connections in the KG and the storage and analysis of query results are straightforward; however, for complex queries, these capabilities become exponentially more challenging with each increase in complexity of the query. For instance, one relatively complex query can yield a KG with hundreds of thousands of query results. Thus, the ability to efficiently query, store, rank and explore sub-graphs of a complex KG represents a major challenge to any effort designed to exploit the use of KGs for applications in biomedical research and other domains. We present Reasoning Over Biomedical Objects linked in Knowledge Oriented Pathways as an abstraction layer and user interface to more easily query KGs and store, rank and explore query results.Availability and implementationAn instance of the ROBOKOP UI for exploration of the ROBOKOP Knowledge Graph can be found at http://robokop.renci.org. The ROBOKOP Knowledge Graph can be accessed at http://robokopkg.renci.org. Code and instructions for building and deploying ROBOKOP are available under the MIT open software license from https://github.com/NCATS-Gamma/robokop.Supplementary information Supplementary data are available at Bioinformatics online.

Volume-based large dynamic graph analysis supported by evolution provenance

We present an approach for the visualization and interactive analysis of dynamic graphs that contain a large number of time steps. A specific focus is put on the support of analyzing temporal aspects in the data. Central to our approach is a static, volumetric representation of the dynamic graph based on the concept of space-time cubes that we create by stacking the adjacency matrices of all time steps. The use of GPU-accelerated volume rendering techniques allows us to render this representation interactively. We identified four classes of analytics methods as being important for the analysis of large and complex graph data, which we discuss in detail: data views, aggregation and filtering, comparison, and evolution provenance. Implementations of the respective methods are presented in an integrated application, enabling interactive exploration and analysis of large graphs. We demonstrate the applicability, usefulness, and scalability of our approach by presenting two examples for analyzing dynamic graphs. Furthermore, we let visualization experts evaluate our analytics approach.

Deterministic Graph Exploration with Advice

We consider the fundamental task of graph exploration. An n -node graph has unlabeled nodes, and all ports at any node of degree d are arbitrarily numbered 0,…, d −1. A mobile agent, initially situated at some starting node v , has to visit all nodes and stop. The time of the exploration is the number of edge traversals. We consider the problem of how much knowledge the agent has to have a priori , to explore the graph in a given time, using a deterministic algorithm. Following the paradigm of algorithms with advice , this a priori information (advice) is provided to the agent by an oracle , in the form of a binary string, whose length is called the size of advice . We consider two types of oracles. The instance oracle knows the entire instance of the exploration problem, i.e., the port-numbered map of the graph and the starting node of the agent in this map. The map oracle knows the port-numbered map of the graph but does not know the starting node of the agent. What is the minimum size of advice that must be given to the agent by each of these oracles, so that the agent explores the graph in a given time? We first determine the minimum size of advice to achieve exploration in polynomial time. We prove that some advice of size log log log n − c , for any constant c , is sufficient for polynomial exploration, and that no advice of size log log log n −ϕ ( n ), where ϕ is any function diverging to infinity, can help to do this. These results hold both for the instance and for the map oracles. On the other side of the spectrum, when advice is large, there are two natural time thresholds: Θ ( n 2 ) for a map oracle, and Θ ( n ) for an instance oracle. This is because, in both cases, these time benchmarks can be achieved with sufficiently large advice (advice of size O ( n log n ) suffices). We show that, with a map oracle, time Θ ( n 2 ) cannot be improved in general, regardless of the size of advice. What is then the smallest advice to achieve time Θ ( n 2 ) with a map oracle? We show that this smallest size of advice is larger than n δ , for any δ < 1/3. For large advice, the situation changes significantly when we allow an instance oracle instead of a map oracle. In this case, advice of size O ( n log n ) is enough to achieve time O ( n ). Is such a large advice needed to achieve linear time? We answer this question affirmatively. Indeed, we show more: with any advice of size o ( n log n ), the time of exploration must be at least n ϵ , for any ϵ < 2, and with any advice of size O ( n ), the time must be Ω( n 2 ). We finally look at Hamiltonian graphs, as for them it is possible to achieve the absolutely optimal exploration time n −1, when sufficiently large advice (of size o ( n log n )) is given by an instance oracle. We show that a map oracle cannot achieve this: regardless of the size of advice, the time of exploration must be Ω( n 2 ), for some Hamiltonian graphs. However, even for the instance oracle, with advice of size o ( n log n ), optimal time n −1 cannot be achieved: Indeed, we show that the time of exploration with such advice must sometimes exceed the optimal time n −1 by a summand n ϵ , for any ϵ < 1.