- 1 -

* binary data(01)

- 관계의 유무

: 동맹/외교관계 유무

: IO/협정 가입 여부

* ordinal/valued data(02)

- 관계의 정도(tie strength)

: 동맹 강도

: IO/협정 가입 중복도

* directed/asymmetric data(03)

- 노드 간의 방향성

: sender-receiver 차이

: 호감도, flow

정세연(2011.3.5)

김치욱

사회연결망분석(SNA) 기초

- gravity(mass-based) model vs. network(relation-based) model

I. ‘관계’ 데이터의 유형

- 2 -

II. 그래프

<data02>

<data03>

- 3 -

<data03 - subgroups>

- faction(cluster, bloc, core)

: 네트워크 내에서 더 긴밀하게 연결돼 있는 노드의 집합

: 미국 네트워크 속에서 중국식 네트워크, 글로벌 네트워크 속에서 지역 네트워크

III. 네트워크 기본 지표

- density

: the proportion of all possible ties that are actually present

: 노드간 정보 확산 속도, social capital의 수준 등에 영향 미침

- reachability

: tie strength에 관계없이 각 노드에 도달할 수 있는 가능성

: data02 --> data01

- connectivity

: the number of nodes that would have to be removed in order for one actor to

no longer be able to reach another.

: 특정 두 노드를 연결해주는 경로가 많고 다양할수록 연결성이 높음(복합동맹?)

: dependency, vulnerability 지표

- reciprocity

: asymmetric(directed) data의 경우, 노드 간 화살표 공유 정도

: degree of institutionalized horizontal connection

- 4 -

- overall clustering coefficient = the

average of the densities of the

neighborhoods of all of the actors.

- weighted clustering coefficient = weight

to the neighborhood densities proportional

to their size

- Clustering coefficient of Guatemala = 3

ties of 3 neighborhoods = 100%

1. Size. Size of ego network.

2. Ties. Number of directed ties.

3. Pairs. Number of ordered pairs.

4. Density. Ties divided by Pairs.

5. AvgDist. Average geodesic distance.

6. Diameter. Longest distance in egonet.

7. nWeakComp. Number of weak components.

8. pWeakComp. NWeakComp divided by Size.

9. 2StepReach. # of nodes within 2 links of ego.

10. ReachEffic. 2StepReach divided Size.

11. Broker. # of pairs not directly connected.

12. Normalized Broker. Broker divided by number of pairs.

13. Ego Betweenness. Betweenness of ego in own network.

14. Normalized Ego Betweenness. Betweenness of ego in own network.

- transitivity

: 전체 가능한 triads 중 ‘서로 연결된 triads’(A->B, B->C, A->C)의 비율

: transitivity가 높을수록 equilibrium 상태에 근접

- clustering

: local neighborhoods

- ego network

: 'ego' = focal node -> ego-neighborhoods 관계의 지표

- 5 -

- Coordinator

: "coordinator" of actors within the same

group as itself.

- Consultant

: brokering a relation between two

members of the same group, but is not

itself a member of that group.

- Gatekeeper

: B is a member of a group who is at it's

boundary, and controls access of

outsiders(A) to the group.

- Representative

IV. Structural hole & Brokerage

* Structural hole (Ronald Burt)

- B와 C 사이에 연결 부재 = B-C 사이의 구조적 공백 -> A의 위치권력 증대, B-C간 연

결을 위해서는 A를 거쳐야 하기 때문.

- <data02>의 경우

- Guatemala -> Honduras: 0.09, Honduras -> Guatemala: 0.06. 따라서 과테말라의 권력이 더 크

다고 할 수 있음.

* Brokerage (B의 브로커 역할) group

- 6 -

: ego B is in the same group as A, and

acts as the contact point or representative

of the red group to the blue.

- Liaison

: ego B is brokering a relation between

two groups, and is not part of either.

- coordination, gatekeeping, consultation, liaison 등은 node 5, representation은 node

2의 역할이 두드러짐.

- 7 -

Freeman's degree centrality - Actors #5 and #2 have the greatest

out-degrees, and might be regarded as the

most influential.

- joined by Actor #7 when we examine

in-degree.

Bonacich's(beta=+) Bonacich's(beta=-)

* beta = 'attenuation factor' = the effect of

one's neighbor's connections on ego's

power

* positive beta = being connected to

neighbors with more connections

makes one powerful.

* negative beta = If ego has neighbors

who do not have many connections to

others, those neighbors are likely to be

dependent on ego, making ego

more powerful.

- Actors 2 and 6's ties are mostly ties to

actors with high degree, making actors 2

and 6 "weak" by having powerful neighbors.

- Actors 3, 7, and 9 have more ties to

neighbors who have few ties, making them

"strong" by having weak neighbors.

* path distance- "Far-ness" = the sum of the distance from each

ego to all others in the network.

V. 중심성(Centrality) - faces of power

1. Degree centrality

- Actors who have more ties to other actors are less dependent and more

powerful.

- Number of ties that involve a given node; Marginals of symmetric adjacency

matrix

2. Closeness centrality

- Degree centrality의 문제점: only take into account the immediate ties that an

actor has, or the ties of the actor's neighbors, rather than indirect ties to all

others.

- Closeness centrality approaches emphasize the distance of an actor to all others

in the network by focusing on the distance from each actor to all others.

- 8 -

- Actor 6 has the largest sum of geodesic

distances from other actors (inFarness of 22)

and to other actors (outFarness of 17).

* Closeness: reach centrality - 전체 노드 중에서 Actor 5가 가장 짧은 단계에 더 많

은 노드에 도달할 수 있음.

- 모든 노드들은 1단계에서 Actor 7에 도달할 수 있음.

* Closeness: eigenvector - 전체 네트워크 구조 상에서 가장 중심적인 노드를 찾

는 방법.

- “eigenvalue" = The location of each actor with

respect to each dimension. --> The first dimension

captures the "global" aspects of distances among

actors; second and further dimensions capture more

specific and local sub-structures.

* Taylor influence measures - Geodesic (path distance) closeness, eigenvalue

closeness의 문제점: "most efficient" path(the

geodesic)만을 고려.

- 모든 경로를 고려할 필요(Hubbell, Katz, Taylor,

Stephenson & Zelen 등)

- 양의 값: sending > receiving = net influencer

(Actor 7의 경우)

- 음의 값: sending < receiving = negative balance

of influence (Actor 6의 경우)

3. Betweenness centrality

- Betweenness centrality views an actor as being in a favored position to the

extent that the actor falls on the geodesic paths between other pairs of actors in

- 9 -

* Freeman node betweenness - Ask which actors (nodes) are most

central.

- Actors #2, #3, and #5 appear

to be relatively a good bit more powerful

than others.

* Freeman edge(relation) betweenness - Ask which relations are most central,

rather than which actors.

- Without the tie to actor 3, actor 6 would

be largely isolated. 즉 actor 3의 actor 6에

대한 betweenness centrality가 높다는 의미.

* Flow betweenness centrality

- Expands the notion of betweenness

centrality, by assuming that actors will use

all pathways that connect them,

proportionally to the length of the

pathways.

- Measured by the proportion of the entire

flow between two actors (that is, through

all of the pathways connecting them) that

occurs on paths of which a given actor is a

part.

- Actors #2 and #5 are clearly the most

important mediators.

- Actor #3, who was fairly important when

we considered only geodesic flows, appears

to be rather less important.

the network. That is, the more people depend on me to make connections with

other people, the more power I have.

- 10 -

- Actors #5 and #2 appear to be in the middle.

- Many groupings (dyads, triads, ...)

: How separate are the sub-graphs? Do they

overlap and share members, or do they divide or

factionalize the network?

: How large are the connected sub-graphs? Are

there a few big groups, or a larger number of small

groups?

: Are there particular actors that appear to play

network roles? For example, act as nodes that

connect the graph, or who are isolated from groups?

* Identification

- Clique 1, the largest clique, has four

members.

- Actor 1, for example, is adjacent to 2/3 of

the members of clique 5.

* Clique co-membership

- Interested in the extent to which these

sub-structures overlap, and which actors are

most "central" and most "isolated" from the

cliques.

- Actor #6 is a complete isolate.

- Actors #2 and #5 overlap with almost all

other actors in at least one clique.

VI. Sub-groups & Equivalence classes

1. Subgroups

- 'bottom-up' approach

: Overall structure of the network is seen as "emerging" from overlaps and

couplings of smaller components.

: Attention on the underlying dynamic processes by which actor build networks.

: Ask how solidarity and connection of large social structures can be built up out

of small and tight components, ex. cliques, n-cliques, n-clans, and k-plexes.

: Cliques = a sub-set of a network in which the actors are more closely and

intensely tied to one another than they are to other members of the network.

- 11 -

- Actors #2 and #5 are "closest" in the

sense of sharing membership in five of the

seven cliques.

* Actor co-membership

- the extent to which the cliques overlap

with one another, as measured by the

numbers of members in common.

- cliques 6 and 7 are (a little) separate from

the other cliques.

* Components

- Sub-graphs that are connected within,

but disconnected between sub-graphs.

- If a graph contains one or more

"isolates," these actors are components.

- Given cut-off value of tie strength = 13,

only non-isolate component (made up of

the Democratic Party and the School

Employees union).

* Cutpoints

- Ask: if a node were removed, would the

structure become divided into un-connected

parts?

- Cutpoints may be particularly important

actors, acting as brokers among otherwise

disconnected groups.

- "blocks" = the divisions into which

cut-points divide a graph.

- EDUC a member of both, meaning that if

- 'top-down' approach

: Looking at the whole network, then identify "sub-structures" as areas of the

graph that seem to be locally dense, but separated to some degree, from the rest

of the graph. ex. components, blocks/cutpoints, K-cores, Lambda sets and bridges,

factions, and f-groups.

: Looking for "holes" or "vulnerabilities" or "weak spots" in the overall structure

or solidarity of the network.

- 12 -

EDUC (node 3) were removed, the WRO

would become isolated. => Node 3, then, is

a cut-point.

* Factions

- Each person was closely tied to all

others in their own subpopulation (that is,

all sub-populations are cliques), and there

are no connections at all among

sub-populations (that is, each

sub-population is a component).

- # of factions 설정

- if # = 4 => 4 factions; individuals

(10, 9), a dyad (3, 6).

=> polarity와 그 응집력?

2. Equivalence

- generalizations about social behavior and social structure

- principles that hold for all groups, all organizations, all societies, etc.

- relations among actors -> social roles/positions/categories = "equivalence class"

- 'structural equivalence

: the same relationships to all other nodes -> exactly substitutable

: 2개, {E, F}, {H, I} - structurally equivalent

- 'automorphic equivalence'

: sets of actors can be equivalent by being embedded in local structures that

have the same patterns of ties - "parallel" structures

: 5개, {A}, {B, D}, {C}, {E, F, H, I}, {G} - different faces, identical structures

- 'regular equivalence'

: the same profile of ties with members of other sets of actors that are also

regularly equivalent

: the same kinds of relationships with some members of other sets of actors.

- 13 -

: 3개, {A}, {B, C, D}, {E, F, G, H, I} - number of classes

VII. 결론

- 데이터 문제

: 기존 데이터의 활용 - dyadic, membership data

: 새로운 데이터의 발굴 - 새로운 관계 개념 개발

- 국가전략

: 기존 네트워크 하에서, or 가상 네트워크 하에서 중심성 등의 변화에 관심