Weighted Simplicial Complex: A Novel Approach for Predicting Small Group Evolution

Sharma, Ankit; Moore, Terrence J.; Swami, Ananthram; Srivastava, Jaideep

doi:10.1007/978-3-319-57454-7_40

Cited by 8 publications

(10 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…• Finally, one could take into account changing preferences, attitudes, or opinions of the agents over time. This evolutionary model can even be applied to weighted complexes [10,21,39] and could potentially be used to quantify the stability of political structures over time and track the influence of mediators or the development of coalition patterns. This could also be combined with some of the above considerations; for example, one could define a time-series power index of an agent over an issue or a set of issues.…”

Section: Stab(p ) ≤ Stab(cp )mentioning

confidence: 99%

Political structures and the topology of simplicial complexes

Mock¹,

Volic²

2021

Preprint

View full text Add to dashboard Cite

We use the topology of simplicial complexes to model political structures following [1]. Simplicial complexes are a natural tool to encode interactions in the structures since a simplex can be used to represent a subset of compatible agents. We translate the wedge, cone, and suspension operations into the language of political structures and show how these constructions correspond to merging structures and introducing mediators. We introduce the notions of the viability of an agent and the stability of a political system and examine their interplay with the simplicial complex topology, casting their interactions in category-theoretic language whenever possible. We introduce a refinement of the model by assigning weights to simplices corresponding to the number of issues the agents agree on. In addition, homology of simplicial complexes is used to detect non-viabilities, certain cycles of incompatible agents, and the (non)presence of mediators. Finally, we extend some results from [1], bringing viability and stability into the language of friendly delegations and using homology to examine the existence of R-compromises and D-compromises. Contents 14 5.2. Stability of political structures 17 5.3. Merging and mediating political structures 18 5.4. Weighted simplicial complex model 20 5.5. Homology and political structures 23 6. Delegations and compromises 25 7. Future directions 28 References 29

show abstract

Section: Stab(p ) ≤ Stab(cp )mentioning

confidence: 99%

Political structures and the topology of simplicial complexes

Mock¹,

Volic²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…For one, hypergraphs contain two distinct sets of entities: vertices and hyperedges. In general, these two sets can differ significantly in terms of their size, skew in cardinality/degree 6 , and associated computation. Further, MESH computation runs on only one of these sets at a time.…”

Section: A Representationmentioning

confidence: 99%

“…Since such group-based phenomena involve multi-user interactions, it has been shown that many natural phenomena can be better modeled using hypergraphs than by using graphs [5] ranging from large-scale social graphs [6] to disease-gene networks [7]. As a result, there is a growing need for scalable hypergraph processing systems that can enable easy implementation and efficient execution of such algorithms on real-world data.…”

Section: Introductionmentioning

confidence: 99%

MESH: A Flexible Distributed Hypergraph Processing System

Heintz

Hong

Singh

et al. 2019

2019 IEEE International Conference on Cloud Engineering (IC2E)

View full text Add to dashboard Cite

With the rapid growth of large online social networks, the ability to analyze large-scale social structure and behavior has become critically important, and this has led to the development of several scalable graph processing systems. In reality, however, social interaction takes place not only between pairs of individuals as in the graph model, but rather in the context of multi-user groups. Research has shown that such group dynamics can be better modeled through a more general hypergraph model, resulting in the need to build scalable hypergraph processing systems. In this paper, we present MESH, a flexible distributed framework for scalable hypergraph processing. MESH provides an easy-to-use and expressive application programming interface that naturally extends the "think like a vertex" model common to many popular graph processing systems. Our framework provides a flexible implementation based on an underlying graph processing system, and enables different design choices for the key implementation issues of partitioning a hypergraph representation. We implement MESH on top of the popular GraphX graph processing framework in Apache Spark. Using a variety of real datasets and experiments conducted on a local 8-node cluster as well as a 65-node Amazon AWS testbed, we demonstrate that MESH provides flexibility based on data and application characteristics, as well as scalability with cluster size. We further show that it is competitive in performance to HyperX, another hypergraph processing system based on Spark, while providing a much simpler implementation (requiring about 5X fewer lines of code), thus showing that simplicity and flexibility need not come at the cost of performance.1 In this paper, we use "graph" to refer to a traditional dyadic graph.

show abstract

“…In applications, however, simplicial complexes are often weighted: for instance, in scientific collaboration networks, teams of collaborators can be weighted by a measure of the strength of their collaboration (e.g., [5]). Recently, weighted simplicial complexes have become popular in topological data analysis (TDA) to study weighted cloud data by replacing the data with a family of weighted simplicial complexes (see [5,10,28]).…”

Section: Introductionmentioning

confidence: 99%

On algebraic and combinatorial properties of weighted simplicial complexes

Kara

2020

Preprint

View full text Add to dashboard Cite

Weighted simplicial complexes (WSCs) are powerful tools for describing weighted cloud data or networks with weighted nodes. In this paper, we propose a novel approach to study WSCs via the concept of polarization. Polarization of a WSC allows one to construct a new (unweighted) simplicial complex which coincides with an object called the mixed wreath product. This new construction preserves several properties and invariants of the underlying simplicial complex of a WSC. Our main focus is to analyze WSCs through their underlying simplicial complexes and mixed wreath products. Combinatorially, we investigate properties such as vertex-decomposability, shellability, constructibility; algebraically, we study Betti numbers, associated primes and primary decompositions of ideals associated to WSCs.

show abstract

Weighted Simplicial Complex: A Novel Approach for Predicting Small Group Evolution

Cited by 8 publications

References 9 publications

Political structures and the topology of simplicial complexes

Political structures and the topology of simplicial complexes

MESH: A Flexible Distributed Hypergraph Processing System

On algebraic and combinatorial properties of weighted simplicial complexes

Contact Info

Product

Resources

About