Graph Theoretic Model for Community Wireless Networks

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A Graph Theoretic Approach for Analysis and Design of Community Wireless

Networks

Abdelnasser M. Abdelaal and Hesham H. AliDepartment of Computer Science

College of Information Science and TechnologyUniversity of Nebraska at Omaha

Omaha, NE 68182{aabdelaal | hali}@mail.unomaha.edu

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Agenda

Introduction Graph Modeling Proposed Graph Theoretic Model Significance of Research Conclusion


What are Community Wireless Networks

It is about “digital inclusion:” The world Internet penetration is 20.0 %.

Government solutions may not be applicable Commercial Internet solutions are not viable for communities that have:

Low income, limited population density, remote locations, harsh geography.

The overall objective is to improve the socio-economic well-being of the community at large.

A simple CWN: When two neighbors, friends, family members, or roommates share an

access point.

A citywide CWN: When a big community (or municipality) shares a few access points. It could grow, or concatenate with other WiFi hotspots, to form a city-wide

wireless network.

What are Community Wireless Networks, Cont.

Definition: CWNs are wireless networks owned, built and operated by the local

community for the purpose of providing affordable or free wireless access They are built by the shared resources of communities (e.g., times, effort,

money donations, skills, beliefs, values and computing resources. They are value networks where digital resources are brokered:

Commercial values Non-commercial values

Similar wireless networks: Municipal wireless WiFi hotspots Private wireless LANs

Private WLANs Municipal Wireless CWNs


Issues of CWNs Issues of CWNs:

CWNs are complex systems with several social, economic, and technical variables.

There is a lack of theories and general models that describe and analyze these emerging networks

CWNs are mixed with municipal wireless networks, and public WiFi hotspots

Literature has been influenced by computer geeks and non academicians.

How can we measure the contributions and the benefits of stakeholders

The Objective: Using graph theory to describe and analyze CWNs and solve related

problems. We used a socio-technical approach is used to find the Internet

connectivity solution that fits a specific social group

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Developing a Wireless Network Suitable for a Specific Social Network

The social graph supported by the CWN The wireless graph that serves the community

Will the attributes of the community determine the suitable connectivity solution ?

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Why Graph Theory

Why graph concepts? We can tie the social resources with technical resources in a single artifact The distance between local residents and the connection between them is

important for coverage issues and antenna placement The properties ( social ties, trust, distance, density) of the social group

determine the most suitable solution and technology (ad-hoc, infrastructure BSS, extended service set).

In a classic village or neighborhood, “everyone knows everyone else” and it is easier for them to share a wireless network.

Actors are more likely to be connected with one another if they are geographically near to one another.

CWNs represent a new form of complex networks They represent collective actions in the digital domain similar to open source

software development


What is a Graph?

A graph is a mathematical model G(V,E) comprises a set V of vertices and a set E of edges. The node set could be anything. The set of edges represent ties between nodes. If there is a tie between a and b, then {a,b} ⊆ E : a,b ∈V and a≠b}. then we say vertices a and b are adjacent and the edge {a, b} joins them or connects them or is

incident on them. Two edges that share one vertex, such as {a,b} and {b,c} with a≠c, are adjacent to each other. Edges could have weights, the weight of {a,b} is 5. Vertex {f} is isolated We have three components {f}, {h, g}, {a, b, c, d, e}

a

b

cd

e

f

h

g

5


What can graphs model? Health Care

Health support systems, spread of diseases

Computer Science[ Cost of wiring computer networks Analyzing peer-to-peer networks Analyzing online social networks (e.g., emails, blogs, MySpace)

Management Science Corporate strategic alliances, organizational hierarchy Information flows, trade, partnerships

Social Science Neighboring behavior, community participation, civic engagement Children groups, friendship, high school cliques Work teams, voluntary associations, social movements Social contacts (kinship, terrorism, crime networks)

Economics and Finance Financial networks Good exchange, market contracts, and trade agreements

Many other applications in anthropology, transportation, biology

The world is composed of networks

04/12/23 Amcis2008

Community Wireless Community Wireless NetworksNetworks

Computer ScienceComputer Science

Management Management ScienceScience

Social ScienceSocial Science

EconomicsEconomics

and Financeand Finance

CWNs: A Multidisciplinary Approach

CWNs are socio-technical networks

There is a heavy confluence between social, economic, and technical variables

We can model them in a single artifact


Proposed Graph Theoretic Model

.

Outputs

Inputs

Volunteerism, donations, partnerships, node hosting, OSS, frequency regulation, social ties and values

CWNsValue proposition, incentives, management, ownership, pricing, funding, acceptance

QoS, security, reliability, node placement, coverage, data rate, signal interference

Tech factors Social factors

Graph theory

Physical capital, social capital and human capital

Variables of CWNs

Implementation phase

Operation phase Educational, commercial, medical, municipal, societal, and personal services

Mobility, affordability, time and effort savings, resource sharing

Social and economic development


A Graph Theoretic Model for CWNs, cont.

Each CWN is composed of a wireless graph ( or network) that serves a social graph

The wireless graph: The wireless network is a directed graph Gw = (Vw, Ew) Its nodes are workstations, routers, extenders, etc Its links are the wireless signals These links have attributes such as bit rate, packet delay, packet loss, security, etc

The social graph: The community is represented by a directed graph Gs (Vs, Es), Its set of nodes Vs represents actors or CWNs Its set of edges Es represent the social ties and interactions between these stakeholders. These ties could be kinship, neighborhood, collaboration, friendship, reciprocation, trust, etc. Vs has three categories of actors: beneficiaries, contributors, and isolated nodes. Edges are weighted by the contributions and the benefits of participants. Benefits include free Internet access, donated PCs, technical expertise, exposure, or spiritual benefits. Contributions include voluntary work or technical skills, donating money or old equipment, hosting a wireless

node.

The confluence and interaction between these two graphs determine the functionality of CWNs

Advantages of this Model It provides the vocabularies, concepts and the mathematical operations that could be

used to label, denote, quantify and measure variables of CWNs; It gives us the ability to prove theories and deduce testable statements related to

CWNs as complex networks. We can determine who are the main actors in the network? Who has control over what flows in the network? We can identify the location with best visibility to install the facilities We can cluster nodes in a way that provides better coverage and higher performance We can identify bottlenecks or central nodes that provide the only connection

between different parts of the network. We can measure the flows of tangible (e.g., donations) and intangibles (e.g., trust,

social cohesion, influence, knowledge) in the network We can identify isolated nodes It shows the importance of structural properties of communities while developing

CWNs

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Modeling Stakeholders of CWNs

Stakeholders of CWNs: Community members, Volunteers, municipalities, businesses, technology vendors, nonprofit

organizations, open source software developers, academic institutions, students, churches, etc. These stakeholders could be classified into beneficiaries, contributors, and isolates.

Their contributions: Donations, partnerships, volunteerism, technical skills, sharing a wireless signal with others. These contributions represent the role of social communities in building and sustaining their own

wireless networks

Their benefits: Providing free Internet access to bridge the digital divide; Improving the business opportunities in the area; Improving the civic engagement and political participation; Supporting municipal services Obtaining technical expertise Gaining publicity and exposure Improving the well-being of the community at large.

We can use concepts of graph theory to measure their contributions and benefits? This is important to empower them and engage them in building and maintaining these networks

Modeling The Omaha Wireless Network

Washington Library

Elmwood Park

UNO

Rosenblatt Stadium

PKI Students Omaha community

Vendors Municipalities

PKI - Experience , free internet

Free internet, old PCs, civic engagement

Publicity Reputation

Students Reputation - Technical skills 0

community Publicity Exposure - Publicity Reputation

Tech. vendors Access points 0 Access points - 0

Municipalities Access to public places

0 0 - -

Micro-Macro level of analysis

We view the Omaha wireless network as a value network

The columns represent benefits and the rows represent contributions of different actors

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Determining Where to Install the Access Point

A central actor is the one that is involved in many ties. The PKI is the graph center We installed access points at PKI because of its high centrality The administration unit is also hosted by PKI because of its high centrality

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Modeling Community Contributions to Build the Network

A matrix is a different way to represent a graph

If the cell value is “1”, the network receives this type of contribution and vis versa

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Modeling Community Contributions to Build the Network, Cont.

We can classify contributors of CWNs and measure their contributions

Green nods represent contributors and red nods represent IDs of CWNs

Main actors are volunteers, advocates, and money donors in different CWNs

The edges are weighted by the value of their contributions

This is important to reciprocate them and empower similar actors

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Modeling Community Contributions to Build the Network, Cont

time money Tech.support Sharing OSS Other

Time 1 0.06 0.46 0.59 0.3 0.22

Money 0.06 1 0.06 0.2 0.28 0.2

tech.support 0.46 0.06 1 0.23 0.3 0.22

Sharing 0.59 0.2 0.23 1 0.13 0.18

develop software 0.3 0.28 0.3 0.13 1 0.46

Other 0.22 0.2 0.22 0.18 0.46 1

The Similarity Matrix between Different Types of Community Contributions


Significance of Research

For practitioners: This model expands the problem solving abilities of CWNs practitioners. It helps them to distinguish CWNs from municipal wireless networks

and commercial WiFi hotspots It helps communities to assess their potential resources that could be

mobilized to develop a community-centric wireless network For researchers:

This graph representation of CWNs provides a rich set of conceptual measures and insights to guide current and future research related to community and municipal wireless networks.

It helps us to solve a number of key problems using well defined algorithms such as identifying proper places for positioning access points using the concept of graph centers or finding the best grouping of nodes in the network using the concept of clustering in graphs.


Significance of Research, Cont. The model limitations:

It is difficult to aggregate the tangible and intangible benefits and contributions of CWNs’ actors.

It is difficult to include all actors in the study. CWNs are networks not systems

Current and future work: Addressing the impact of the social variables (e.g., community size, density of the network,

and types of used applications) on the technical factors such as signal interference, QoS, throughput, and the optimal network size.

Measuring the role of CWNs in generating social capital and human capital. Measuring the trust in the domain of CWNs

The originality of our research : Modeling CWNs in a single artifact We consider the multidisciplinary nature of CWNs Economic flows, social networks, and computer networks are interrelated in CWNs The tangible and intangible contributions and benefits of CWNs stakeholders have

measurable economic value


Conclusion We view a CWN as two graphs: a social graph and a wireless

graph. We used graph concepts to model and attribute CWNs CWNs are value networks where digital resources are brokered

among community members The attributes and the interactions between the components of these

two graphs determine different aspects of CWNs. This quantitative artifact helps us to study CWNs and measure their

related variables It helps us to decide where to install the access point or router It helps us to classify the stakeholders of CWNs and identify their

contributions and benefits. Future work will focus on measuring the role of CWNs in creating

social and human capital

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Graph Theoretic Model for Community Wireless Networks

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