University of Southern Denmark

Political fragmentation and alliances among armed non-state actors in North and WesternAfrica (1997-2014)

Walther, Olivier; Leuprecht, Christian; Skillicorn, David

Published in:Terrorism and Political Violence

DOI:10.1080/09546553.2017.1364635

Publication date:2020

Document version:Accepted manuscript

Citation for pulished version (APA):Walther, O., Leuprecht, C., & Skillicorn, D. (2020). Political fragmentation and alliances among armed non-stateactors in North and Western Africa (1997-2014). Terrorism and Political Violence, 32(1), 167-186.https://doi.org/10.1080/09546553.2017.1364635

Go to publication entry in University of Southern Denmark's Research Portal

Terms of useThis work is brought to you by the University of Southern Denmark.Unless otherwise specified it has been shared according to the terms for self-archiving.If no other license is stated, these terms apply:

• You may download this work for personal use only. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying this open access versionIf you believe that this document breaches copyright please contact us providing details and we will investigate your claim.Please direct all enquiries to puresupport@bib.sdu.dk

Download date: 28. Jul. 2022

1

Political Fragmentation and Alliances among Armed Non-State Actors in North and

Western Africa (1997-2014)

Olivier Walther a,b, Christian Leuprecht c,e and David B. Skillicorn d aUniversity of Florida, Center for African Studies, Gainesville, Florida; bUniversity of Southern

Denmark, Department of Political Science, Sønderborg, Denmark; cRoyal Military College of

Canada, Political Science, Kingston, Ontario, Canada; dQueen’s University, School of

Computing, Kingston, Ontario, Canada; eCollege of Business, Government & Law, Flinders

University of South Australia

TERRORISM AND POLITICAL VIOLENCE

2020, VOL. 32, NO. 1, 167–186

https://doi.org/10.1080/09546553.2017.1364635

Abstract

Drawing on a collection of open source data, the article uses network analysis to represent

alliances and conflicts between 179 organizations involved in violence in North and Western

Africa between 1997 and 2014. Owing to the fundamentally relational nature of internecine

violence, this article investigates the way the structural positions of conflicting parties affect their

ability to resort to political violence. To this end, we combine two spectral embedding techniques

that have previously been considered separately: one for directed graphs that takes into account

the direction of relationships between belligerents, and one for signed graphs that takes into

consideration whether relationships between groups are positive or negative. We hypothesize

that groups with similar allies and foes have similar patterns of aggression. In a region where

alliances are fluid and actors often change sides, the propensity to use political violence

correspond to a group’s position in the social network.

Introduction

In a recent letter addressed to the President of the Islamic Council of Mali on 27 September

2016, Iyad ag Ghaly, the leader of the jihadist group Ansar Dine, announced that he would

unilaterally cease attacks throughout Mali “and especially in the North of the country”. Signed

This is an Accepted Manuscript of an article published by Taylor & Francis in Terrorism and Political Violence on September 26th, 2017, available online: http://www.tandfonline.com/10.1080/09546553.2017.1364635

2

on behalf of “Ansar Dine and its allies”, the letter further explained that the group would not

renounce its goal of imposing Islamic law (sharia) but would work towards a ceasefire to “ensure

the security of persons and their property and promote social cohesion, a guarantee of peace and

stability”1.

The letter arrived one month before Ansar Dine attacked a UN convoy in the north of the country

(RFI 2016). The subject of much debate, this is the latest development in a tortuous military

career for ag Ghaly, who, since the 1990s, has been a mercenary for the late Col. Gaddafi, rebel,

negotiator for the Malian government, consular officer in Saudi Arabia, leader of a terrorist

group, and fugitive. The fact that a militant such as him has successively worked for and against

the state, within Mali and abroad, and as a civilian and a military leader, illustrates just how fluid

many modern African conflicts are: commanders and rank-and-file fighters frequently shift

allegiances among regular forces and armed non-state actors. A similar volatility characterizes

political allegiances between governments and myriad often ephemeral armed groups, who split

and coalesce as new opportunities arise. While groups that appear at odds one day may be allies

the next, splinter groups formed after leaders fall out with one another might nonetheless

collaborate against a third party.

The complex motivations and outcomes of such alliances and conflicts have received growing

attention over the last decade2. On the one hand, a number of detailed qualitative studies have

contributed to documenting how relationships among rebels, religious extremists and traffickers

that developed in North and Western Africa were mainly based on corruption around illegal

flows of drugs, weapons and migrants3 and had fundamentally changed the political landscape of

the region4. Mali, with its many short-lived alliances between secessionist and Islamist groups

with conflicting agendas, has been of particular interest5. On the other hand, a growing body of

quantitative studies identifies internal fragmentation, conflicts and alliances between armed

groups as a crucial explanation for the onset and diffusion of internecine violence6 and often

elusive quest for peace settlements7.

This article bridges these strands of literature through a more formal approach to social networks

of belligerents in the region. Examining the relationships between alliances and conflicts as a

3

putative explanation for the patterns of violence in North and Western Africa, the article posits a

relational approach to the study of the structure of relationships among state and non-state actors.

In doing so, it builds on a growing body of literature that takes advantage of the recent

availability of disaggregated data to map and model ties between and within violent

organizations8.

The article proceeds as follows. The second section reviews the literature on conflict and signed

networks and shows that greater access to geo-referenced data and the use of spatial statistical

analysis has advanced the study of patterns of armed groups over the past decade. The third

section presents the data and explains how we structured them into networks of belligerents. The

fourth section models the structural position of actors in conflict. The last section addresses the

implications of the findings for theory, method, and practice.

Previous Research on Conflicts and Signed Networks

While past analyses of (civil) wars were limited by a lack of reliable data, the proliferation of

satellite and disaggregated data has spawned innovative approaches to investigating the onset

and diffusion of political violence across time and space 9. The concomitant proliferation of

political and economic predictors, on which the spatial-analytical approach can draw, now

includes factors as diverse as the nature of government, ethnic divisions, poverty, income,

inequality, number and morale of troops, frequency of droughts, and endowment of natural

resources10.

Some factors that may explain why groups resort to violence are also related to the structure of

relationships that connect actors in conflict11. Modern African conflicts bring together a

multitude of state and non-state belligerents that include regular military forces, pro-government,

ethnic and religious militias, rebels, secessionist and self-determination movements, violent

Islamist groups, warlords, thugs and criminals12. The relationships within and between these

actors are often characterized by a bewildering array of alliances and conflicts13. In North and

Western Africa, for example, the Salafist Group for Preach and Combat (GSPC) – a splinter

group of the Algerian Armed Islamic Group – rebranded itself as AQIM in 2007. Some of its

members broke off in 2011 to form MUJAO while others formed Al Moulathamoun and Al

4

Mouakaoune Biddam. In 2013, MUJAO merged with Al Moulathamoun to form Al

Mourabitoune, which, in 2015, was renamed Al Qaeda in West Africa. More recently, AQIM,

Ansar Dine, Al Mourabitoun and the Macina Liberation Front merged to form the “Group for the

Support of Islam and Muslims” (Jama’at Nusrat al-Islam wal-Muslimin)14. These mergers, splits

and name change suggest that organizations affiliated with Al Qaeda share a common historical

and ideological background and form several components of a single, opportunistic network,

rather than independent entities. Causes and consequences of the patterns of violence associated

with such alliances and conflicts have received increasing attention over recent years15.

Research focusing on intragroup dynamics suggests that the internal structure of warring factions

is central to explaining patterns of violence of non-state actors, be they insurgents16 or

terrorists17. Social ties forged before and during war between belligerents make violent

organizations more cohesive, less prone to factionalization, and facilitate recruitment and

allegiance during conflicts. Internal divisions in self-determination movements are associated

with a greater probability of civil wars because the multiplication of belligerents creates political

uncertainties as to what concessions could be made and what commitments could resolve a

conflict through non-violent means18. Internally divided self-determination movements are also

more likely to receive concessions than unitary ones because states often “divide and concede”

rather than “divide and conquer”19. While fragmented groups seem to increase the intensity of

violence, particularly against civilians20, the effect of the fragmentation of violent groups on the

duration of conflicts remains controversial. Some studies suggest that fragmentation complicates

peace settlements by multiplying the number of ‘veto players’ that must approve a settlement21.

Others argue that fragmentation accelerates them by weakening belligerents and forcing them to

cooperate22.

Studies focusing on intergroup dynamics suggest that violence between non-state actors can be

understood as a mean for access to resources and political leverage to fight central

governments23. This explains why rebel groups often fight each other instead of forming

coalitions24, particularly when the government lacks repressive power25. Research on armed

conflict between non-state actors shows that inter-rebel violence is more likely in drug

production areas, where rebel groups have established control over territory beyond the

5

government’s reach and are numerically strong, and where states are unable to exercise their

authority26. That intergroup alliances also shape the outcome of civil wars is less documented.

While intergroup alliances rarely lead to victory, interdependencies between rebel groups bring

valuable resources such as intelligence and tactical support that can be used against a well-

organized and capable government to avoid defeat27. In conflict situations where an external

party, such as a foreign military power, can enforce cooperation between warring parties that

leads to a peace settlement, armed groups might have an interest in forming coalitions and

aligning with the side they believe to have the greatest chance of emerging victorious28.

Recent studies on fragmentation and alliances among state and non-state actors approach

violence as a relational process whose structure enables and constrains action29. Other network

analysis has already observed that social actors who wish to reduce their structural constraints

can develop network tactics to alter the structure - rather than the behavior of others -- to their

advantage30.The ready availability of disaggregated data, combined with recent conceptual and

computational advances in network analysis has allowed a growing number of studies to test

such assumptions empirically using social network analysis (SNA). SNA is the study of

individual actors, groups, organizations or countries, represented by the nodes of the network,

and the relationships between these actors, represented by their links. As both a paradigm of

social interactions based on graph theory and a method, SNA seeks to understand networks by

mapping out the ties between nodes as they are rather than how they ought to be or are expected

to be31.

SNA is particularly adept at capturing the complexity of conflict situations due to its ability to

describe, represent, and model signed networks, i.e. networks that contain both positive and

negative relations. Positive ties develop to overcome collective-action problems, enforce trust

and ideology, coordinate activities at a distance, distribute resources, or disseminate ideas and

decisions. Alliances between states are typical of positive-tie networks. By contrast, negative ties

develop among actors that dislike, avoid, or fight one another. For positive and negative ties,

SNA can be used to study the structure and function of the network as a whole, and the role of

each node in the group in relation to others. Network approaches have been used to verify

whether states with common enemies have fought one another,32 how alliances or rivalries

6

between states could explain the diffusion of World War I on a global scale and to illustrate the

increasing number of alliances between African states since the end of the Cold War.33

Networks with positive ties are known to be structured differently from those with negative

ties34. Networks based on friendship, alliance and collaboration are denser and more clustered

around actors that share similar values than networks with negative ties, because individuals and

organizations tend to have more friends than enemies35. Positive-tie networks also harness more

resources, ideas, and knowledge than negative-tie networks since the latter are driven by hatred,

avoidance or conflict. As a result, many centrality measures based on the assumption that social

networks serve as conduits for flows of information, advice, or influence, such as betweenness or

closeness centrality, are unrealistic in the case of actors in conflict36. Networks with negative ties

are also well known for their low level of transitivity, a principle that assumes that two actors

that share a connection to a third actor are likely to be connected themselves.

A growing literature suggests that, despite their differences, positive- and negative-tie networks

should be analyzed simultaneously37. One way to incorporate both allies and adversaries is to use

structural balance theory, which argues that social relations are stable if they contain an even

number of negative ties. Stable groups of three actors (known as triads) are theoretically stable if

everyone likes everyone else, or if two actors are in conflict with a third party38. Over time,

unstable triads theoretically evolve towards stable triads, because instability creates tensions that

can only be resolved by altering views, behaviors and alliances. Another approach to signed

networks is to model the structural autonomy and constraints of actors. Smith et al. (2014) argue

that an actor’s political independence is constrained both by its potential to reach other actors’

resources and by the structural position of allies and enemies39. Being connected to a single ally

that is not under threat considerably reduces the autonomy of actors in signed networks, while a

diversified network of allies enhances autonomy.

This article adopts a complementary approach. Instead of assuming that political violence is

explained by attributes of the belligerents or by exogenous factors, we propose that the

propensity to use political violence corresponds to a group’s position in the social network rather

than their actions per se. To this end, the initial part of our analysis aims at representing how

7

armed non-state actors are connected to their allies and enemies. We use centrality measures to

identify subclusters of actors where conflict or cooperation is particularly developed, and

highlight the main structural differences between positive- and negative-tie networks. Since

enemies and allies are inextricably linked in real-life networks, the subsequent analytical part of

the article considers positive and negative ties simultaneously. Spectral embedding techniques

make it possible to place the nodes that represent organizations at the position that best balances

the “pull” of allies against the “push” of enemies. This makes it possible to model the balance

between the relative effects of having allies and foes simultaneously. We also take into account

the fundamentally asymmetric nature of conflicts and consider whether groups attack more or

less than they are attacked. Combining signed and directed networks, we expect groups with

similar allies and foes and similar patterns of aggression to form clusters that correspond to their

structural position in the social network.

Research Design

Our analysis relies on data from the Armed Conflict Location and Event Dataset. ACLED

provides a comprehensive list of political events by country between 1997 and 201440. The fifth

version of the data was used to select 37 armed non-state actors in 21 North and Western Africa

countries41, their allies and their enemies, excluding non-identified Islamist and Libyan militias

(see Appendix 1). The scope was limited to events with the following seven referents: Battle –

no change of territory; Battle – Non-state actor overtakes territory; Battle – Government regains

territory; Riots and protests; Violence against civilians; and Remote violence. This generated a

list of 3231 events comprised of 179 organizations and 27,791 fatalities.

The ACLED dataset describes (up to) four groups in each incident: an attacker (A), a

collaborator in the attack (B), a target (C), and a potentially assisting group that may also be a

secondary target (D). This data is used to build a social network in which the nodes are groups,

with positively weighted directed ties between allies (B to A, and D to C) and negatively

weighted directed ties between adversaries (B to C). For example, on January 12, 2014, clashes

between French troops (A) and Malian troops (B) on the one hand, and Ansar Dine (C) and

MUJAO (D) on the other hand, claimed 11 lives, including Islamist leader Abdel Krim, and left

60 injured (ACLED incident 486MLI). Incidents are aggregated so that the ties between any pair

8

of groups reflect all of their interactions. Ties can be both positive and negative, and in both

directions, between the same two groups. Direction is a proxy for intentionality: a group on the

offensive makes a conscious decision to attack while the defender has no choice, and other

groups must decide whether to join. These decisions reflect a calculus of advantage or

ideological alignment.

The resulting graph is analyzed in two steps. First, we map the networks containing negative and

positive ties separately and analyze the most prominent actors using several centrality measures.

Because negative-tie networks do not serve as conduits for flows of information, advice, or

influence, we use degree centrality, which simply refers to the standardized number of ties each

node has, and eigenvector centrality, which refers to the number of nodes adjacent to a given

node, weighted by centrality, and indicate whether nodes are connected to other well-connected

nodes. For our positive-tie network, we use eigenvector centrality and betweenness centrality,

which measures the number of shortest paths from all nodes to all others that pass through that

node42.

Second, we combine both positive and negative ties into a single network, and embed this

network in a geometric space in such a way that the distance between each pair of points

accurately reflects the balance between the ‘pull’ from collaborating groups and the ‘push’ from

aggression between them. These distances are globally integrated as a function of immediate

neighbors (i.e. actors who cooperate to fight each other) as well as neighbors of neighbors and, in

fact, the structure of the entire graph. This integration makes the process challenging: positive

relationships are naturally transitive (“the ally of my ally could plausibly become my ally”) but

negative relationships are not (the proverbial “enemy of my enemy is my friend” does not

necessarily obtain). The adjacency matrices that describe positive and negative ties combine both

kinds of ties. The representation is then normalized so that well-connected nodes are central and

poorly connected nodes peripheral43. This Laplacian matrix is used to embed the graph in a

geometry where position is meaningful (well-connected nodes are placed centrally), and

proximity represents similarity (similar nodes cluster together). Sets of ‘bad’ armed non-state

actors and (supposedly) ‘good’ governmental forces and civil society tend to form polar

9

opposites in some dimension(s) of the representation. Since proximity represents similarity – and

alliance – distance tends to represent opposition.

A Social Network Analysis of Political Violence

Negative- and positive-tie networks

We start with a graph that represents each organization as a node that is connected to those actors

with which it is in conflict. The size of the nodes in Figure 1 is proportional to the number of ties

(or degree).

Three main clusters emerge: the Nigerian cluster that is polarized by Boko Haram; the Trans-

Saharan cluster that is composed of groups affiliated with Al Qaeda such as GSPC and AQIM

and their enemies; and the Libyan cluster that is composed of myriad Islamist brigades and pro-

government forces. With a density of only 0.023, the network is very sparse, which is typical of

networks that are made up exclusively of negative ties: the number of enemies a group can have

is often more limited than the number of potential allies44. The network also has a low level of

transitivity: in only 1.2% of the triads enemies of enemies are in fact enemies, while in most

cases (98.8%), enemies of enemies are friends. By contrast, recent studies in Syria show that

12% of the triads are intransitive, either because two enemies were opposed to each other or

because friends of friends were actually in conflict, which fuels the political and spatial diffusion

of the Syrian conflict45. Finally, organizations with adverse attributes tend to be in conflict with

one other, a tendency known as heterophily. This can be tested using the E/I index, which

calculates the difference between external and internal ties for each group of actors (government,

rebels, militias, civilians, Islamists, and external forces), divided by the total number of ties. The

E/I index for the network is positive (0.899) and statistically significant (chances of getting the

result right by guessing are less than 1%), which confirms that armed non-state actors clash with

organizations that are not in the same category.

10

Figure 1: Negative ties between organizations involved in violent events, 1997-2014

Note: Isolates are not shown.

In terms of adversaries and victims (Table 1), the bloodiest conflicts have seen civilians in

conflict with state and non-state actors. Boko Haram is by far the bloodiest armed group in the

region: it kills both Nigerian civilians (6409 victims) and military forces (5447) en masse. In

Nigeria, conflicts with unidentified groups (3556 victims), Fulani militias (2446), and the

military (2382) also claimed many civilian victims. Clashes involving the Algerian GIA and

Algerian civilians were particularly deadly in the late 1990s, with 6212 victims reported in the

database. The campaigns of civilian massacres adopted by GIA explain why some of its former

members, such as Hassan Hattab, defected to form GSPC in 1998. Finally, the National

Liberation Army and the Libyan Armed Forces clashed during the Libyan civil war in 2011

11

(1740 victims). More than 1350 victims are also reported as a consequence of NATO military

intervention, mostly civilians. Generally speaking, these figures confirm earlier studies: most

victims of African conflicts were civilians who either died at the hands of state or non-state

armed groups, or from the effects of displacement, malnutrition and disease46.

Table 1. Bloodiest conflicts between actors, 1997-2014

Actor 1 Actor 2 Fatalities

Civilians (Nigeria) Boko Haram 6409

Civilians (Algeria) GIA Armed Islamic Group 6212

Boko Haram Military forces of Nigeria 5447

Civilians (Nigeria) Unidentified armed group (Nigeria) 3556

Civilians (Nigeria) Fulani Ethnic Militia (Nigeria) 2446

Civilians (Nigeria) Military forces of Nigeria 2382

NLA National Liberation Army (Libya) Military forces of Libya 1740

Christian Militias (Nigeria) Muslim militia (Nigeria) 1739

Civilians (Libya) NATO forces 1367

AQIM Military forces of Algeria 1074

Military forces of Cameroon Boko Haram 1005

Source: ACLED. Note: a conflict can result from several events. Only conflicts with more than

1000 fatalities are listed.

As expected, the network is composed of few highly central organizations (Table 2) since being

in conflict with many adversaries simultaneously is widely regarded as a liability rather than an

asset47. Among armed non-state actors, AQIM scores highest on degree and eigenvector

centrality, which indicates that it has the greatest number of enemies and is connected to other

actors that also have many enemies, such as the military and police forces of Algeria. This is an

interesting result: if it is a pure liability to have many enemies, then having enemies that are

themselves involved in many conflicts offers more autonomy to AQIM. The ideal structural

situation for an actor embedded in a signed network is to have enemies that are constrained by

numerous threats that affect the outcomes of military operations, reduce their ability to

coordinate activities across the region, and limit their ability to cooperate to achieve their

12

political or religious goals48. MUJAO, GSPC and GIA also occupy a prominent structural

position due to their conflicts with civilians and armed forces in several countries. Other

prominent actors include Boko Haram, which stands out for being connected to many other

actors who themselves have few connections to one other, and Libyan groups such as Ansar al-

Sharia and Libya Shield Brigade.

Table 2: Top-scoring nodes for selected centrality measures – negative ties

Rank Degree centrality Eigenvector centrality

1 AQIM (0.264) AQIM (0.743)

2 Boko Haram (0.200) MUJAO (0.421)

3 MUJAO (0.136) Military Forces of Algeria (0.289)

4 Ansar al-Sharia (0.120) GSPC (0.257)

5 Ansar Dine (0.096) Ansar Dine (0.229)

Mean 0.024 0.071

Std. Dev. 0.035 0.095

Source: ACLED. Note: Scores are indicated in brackets.

The structure of the network of enemies contrasts starkly with the one showing how

organizations involved in violent events have collaborated across the region. As depicted in

Figure 2, the positive-tie network is divided into three main unconnected groups of allies, one

triad that connects an unidentified armed group to Boko Haram and Ansaru, and three dyads.

The main cluster on the left is structured around North and West African military and police

forces and their civilian allies, which are represented in red and yellow respectively. This cluster

is indirectly connected to some of the main Islamist groups in the region, which are represented

in green, through the secessionist movement MNLA. MNLA resulted from the fusion of a

peaceful organization that was defending the rights of the local Tuareg population, an armed

group involved in several rebellions, an organization inspired by the Salafist ideology, and

Tuareg mercenaries who had formerly been employed in Libya49. MNLA was initially allied

with Ansar Dine before switching sides and fighting alongside the French-led military forces in

2013. The two other clusters are structured around the armed forces of Libya and their pro-

13

government brigades and battalions, the other around Islamist groups and ethnic and communal

militias in Libya. Each cluster has a chain-like structure in which organizations are rather distant

from one another. The Algerian Private Security Forces, for example, are eight steps away from

Al Mourabitoune.

The long path-length distance, low density (0.034) and low clustering coefficient (0.104) of the

network are typical of a structure that is not organized around groups of tightly connected actors.

This suggests that most governmental forces and armed non-state actors tend to build bilateral or

trilateral alliances rather than broad coalitions across the region. The graph also highlights the

lack of regional cooperation between government forces that face similar threats: there is no

reported tie between the military forces of Libya and Algeria, or between the military forces of

Cameroon and Nigeria.

Figure 2: Positive ties between organizations involved in violent events, 1997-2014

14

Source: ACLED. Notes: green nodes refer to Islamist groups, red to government forces, yellow

to civilians, and blue to other actors.

Military and police forces have the highest eigenvector and betweenness centrality, followed by

Ansar al-Sharia and the Shura Council of Benghazi Revolutionaries (BSCR), both of which hail

from Libya (Table 3). Generally speaking, betweenness centrality scores – indicating the

propensity to bridge clusters – are very low, even for top-scoring nodes, which suggests that the

networks contain few exceptional brokers. Only the French military forces play a role in bridging

several African armed forces that would otherwise not be connected, hence their high

betweenness centrality. Once again, the isolation of Boko Haram in Nigeria contrasts sharply

with the network of alliances among other Sahelo-Saharan and Libyan groups.

Table 3: Top-scoring nodes for selected centrality measures – positive ties

Rank Eigenvector centrality Betweenness centrality

1 Military Forces of Nigeria (0.400) Military Forces of France (0.111)

2 Police Forces of Nigeria (0.379) Military Forces of Algeria (0.071)

3 Ansar al-Sharia (0.223) Military Forces of Mali (0.070)

4 Shura Council of Benghazi Revolutionaries

(0.260)

Military Forces of Nigeria (0.062)

5 Military Forces of Libya (0.193) MNLA (0.052)

Mean 0.039 0.012

St. Dev. 0.082 0.022

Source: ACLED. Calculations by the authors. Note: Scores are indicated in brackets.

Spectral embedding

Spectral embedding computes a representation of a graph with edge weights (representing tie

strength) by projecting it into a low-dimensional space in such a way that nodes that are similar

(have many, or strong, edges between them) are placed close to one another. As a consequence,

nodes that are important in the network tend to be embedded close to the center. A spectral

embedding may not be visually clear, in the sense that Figure 2 is, but it is guaranteed,

15

mathematically, to be as accurate as possible in the given dimensionality. The networks we

derive from the ACLED data require extensions of the techniques of spectral embedding because

their edges are directed, and they have both positive and negative weights.50 Once again the

resulting embeddings are guaranteed to be the most accurate possible in the given

dimensionality, given assumptions about the relative importance and positive versus negative

ties. Spectral embeddings are intrinsically inductive techniques; they do not require analysts to

hypothesize variables that might cause ties to form in particular contexts; rather they take data

about which ties actually did form, construct the resulting global social network, and

demonstrate the structure of this network, leaving the analyst to infer plausible explanations from

the structure.

To compute spectral embeddings of the social networks derived from the ACLED data (shown in

Figure 3), initially, for the sake of simplicity, we disregard the direction of the ties. Negative ties

resulting from recorded attacks are shown in red and positive ties resulting from alliances, or at

least common purpose, are shown in green. The general structure is polar opposites that represent

groups whose primary relationship is that they attack or are attacked by groups at the other

extreme. The graph clearly shows how ‘bad’ actors such as Islamist and Jihadist groups are

grouped opposite ‘good’ actors, both violent and non-violent. The contrast is particularly evident

for Boko Haram, and its opposition to governmental forces and civilians from Nigeria and

Cameroon, as well as for GIA-GSPC-AQIM, and its opposition to Algerian armed forces and

civilians. The graph also shows that the attack patterns of GIA, GSPC and AQMI differ

markedly from those of Ansar Dine, MUJAO and Al Mourabitoune, which are located much

closer to the center of Figure 3.

16

Figure 3: Spectral embedding showing positive and negative ties

Any measure that considers a group in isolation is unable to distinguish armed non-state actors

from military or police organizations because both have similar patterns of interaction. We,

therefore, compute measures of outward and inward aggression based not on the number of such

incidents but on the length of the relevant ties in the embeddings. A group’s position in the

embedding reflects its relationships with all of the groups with which it interacts; therefore, the

length of the embedded ties is more revealing than simply the number of attacks. For example,

the distance of a group from the center of the embedding reflects not only how many other

groups attack it (or are attacked by it) but also the extent to which its enemies are similar to one

another (close in the embedding). Thus a long red tie reflects not only the existence and

frequency of attacks, but also their strategic intensity. Figure 4 plots groups at the same positions

as in the spectral embedding presented in Figure 3 but labelled to distinguish their “levels of

aggression”: the difference between the outgoing aggression that each group causes and the

17

incoming aggression to which it is subjected. The points are color-coded: red means a group

generates more aggression than it receives; orange means that the group generates some outgoing

aggression; and green means that there is no outgoing aggression (individual scores are presented

in Appendix 1).

Figure 4: Spectral embedding showing levels of aggression

The vicinity of groups presented in Figure 4 allows us to distinguish armed non-state actors (red,

with almost all neighbors red as well) from national defense forces (red, but with many orange or

green neighbors). In other words, most of the polar opposites are structurally distinct. ‘Bad’ net

aggressors such as AQIM or Boko Haram tend to cluster together, or are isolated; ‘good’

aggressors such as militaries tend to cluster with orange and green groups. Neutral actors such as

the International Committee of the Red Cross (ICRC) tend to fall in the middle and are colored

green. Victims are also green but tend to be located near their champions.

18

Northern Nigeria and Libya are particularly interesting as they involve many armed non-state

actors with strong structural constraints. We would expect Northern Nigeria, where Boko Haram

is particularly dominant, to have more of a dual structure than Libya, where a plethora of violent

groups compete for control of the state and oil resources. Indeed, spectral embedding showing

conflict and cooperation for 37 organizations in Northern Nigeria (Figure 5) clearly confirms that

Boko Haram is in conflict with virtually everyone, a situation comparable to that of Daesh in the

Middle East, which opposes all governments and non-state actors – including Al Qaeda – in the

region.

Figure 5: Spectral embedding showing positive Figure 6: Spectral embedding showing

and negative ties for 37 organization in positive and negative ties for 30

Northern Nigeria organizations in Libya

Note: for the sake of clarity, Ansaru is not shown.

In Libya, spectral embedding conducted on 30 organizations highlights the ongoing conflict

between weak alliances of pro-Islamist groups and weak alliances of pro-government forces

(Figure 6). Islamist groups, on the left of the graph are composed of Islamist militias such as

Libya Dawn and Libya Shield, and of Jihadist groups close to Al Qaeda such as the

Revolutionaries Shura Council (BRSC), a coalition that includes Ansar al-Sharia, the 17

February Brigade, and the Rafallah Sehati Brigade. These groups, based in Tripoli and Benghazi,

19

oppose the Libyan army, as indicated by several long red ties. Among pro-government forces, on

the right, are anti-Islamist militias such as the Zintan Militia, the Al-Sawaiq Battalion and the Al

Qaqa Brigade. Civilians and journalists are located near the internationally recognized authorities

of Libya.

Conclusion

This article has illustrated the effectiveness of extending social network analysis to the structure

of armed non-state actors in North and West Africa, a region which, over the past 20 years, has

become more politically unstable. However, conventional social network measures fail in these

settings. For example, measures such as betweenness are inappropriate because negativity does

not ‘flow’ in the way that positivity is conceived, and centrality is not a crucial property when

negativity separates nodes far from the center. Instead, our methodological contribution is based

on a novel approach that combines signed and directed graphs to highlight opposed groups and

distinguish among several kinds of aggressors as a function of their conflict patterns. In settings

where groups form shifting alliances and oppositions, an approach that takes into account not

only local, pairwise relationships, but also global patterns that emerge, is needed for situational

awareness. Conventional social network analysis can represent positive ties, but not ties where

direction matters, or where ties represent a negative association. Furthermore, these are not

independent properties of a social network and so must be represented together.

In the process, the article advances theory on the fragmentation of conflict. We used open source

data to map how 179 organizations involved in political violence were structurally connected

through conflict and alliances. Our analysis shows the extent to which the network that connects

actors in conflict has a low density, a low level of transitivity, and contains few central actors,

three typical features of negative-tie networks. AQIM is unequivocally the most connected

organization, both in terms of the overall number of actors with which the group is in conflict,

and the respective centrality of its enemies. In network terms, this is a liability. Divided into

several clusters, the positive-tie network has a long path-length distance, low density and low

clustering coefficient, a structure that suggests that most organizations tend to build limited

alliances rather than broad coalitions across the region.

20

We then combined the two networks and modeled the effect of having friends and foes

simultaneously. Using the attack relationships, we also measured the level of outgoing and

incoming aggression of each group. From this approach, five categories emerge: (1) neutral

actors, represented in the middle of our graphs; three kinds of groups that cluster together – (2)

victims, (3) groups that are attacked more than they themselves attack, and (4) groups that

counter violence and thus attack more than they are attacked (e.g. militaries) -- and (5) violent

extremist groups that attack more than they are attacked, such as armed non-state actors. Groups

that are net attackers are indistinguishable at the level of individual behavior, but clearly separate

into pro- and anti-violent extremism based on the groups to which they are close. This

conclusion is in line with our original proposition that the propensity to use political violence

corresponds to a group’s position in the social network rather than their actions per se. This

raises situational awareness in a setting where it may be difficult to distinguish ‘good’ from ‘bad’

actors based on their apparent goals or ideology.

These findings have policy implications for governments and external forces involved in

deterring armed non-state actors. First, unlike their adversaries, armed non-state actors are

connected across the region. In recent years, several ‘Sahel’ strategies have been initiated by

organizations as diverse as the European Union (2011), the United Nations (2013), the Economic

Community of West African States (2014), the African Union (2014), and the regional

coordination framework G5 Sahel, to improve governance, security and development in the

region. Building institutional capacity around common interests is likely to pay off in a region

that is largely devoid of collective security institutions that could help countries coordinate, build

trust, and go beyond ad hoc engagements. Precedent also suggests that states outside the region

will continue to play a supporting rather than a leading role. In addition to supporting capacity-

building efforts already underway, Western governments should be prepared to mount a

comprehensive Whole-of-Government effort in support of local authorities that will minimize

their local footprint, while optimizing outcomes. From a military perspective, the tenuous

personal allegiances in the region call for a mobile and flexible military response. Regional

volatility notwithstanding, operations Serval and Barkhane suggest that desert insurgents are not

impervious to external attack. As Western armies and their African allies become more mobile

21

and flexible in their regional responses to political violence, desert insurgency proves to be a

double-edged sword that can also work against those who know the terrain best.

22

Appendix 1. Violent political organizations, 1997-2014

Abu Obeida Brigade

Abu Salim Martyrs’ Brigade

Al Qaeda

Al Qaqa Brigade

Al-Burayqah Martyr’s Brigade

Al-Salafiya

Al Jihadia

Ansar al-Sharia

Ansar Dine

Ansaru

AQIM: Al Qaeda in the Islamic Maghreb

Boko Haram

Brega Martyrs Brigade

El-Farouk Brigade

Falcons for the Liberation of Africa

February 17 Martyrs Brigade

Fighters of The Martyrs Brigade

FIS: Islamic Salvation Front

GIA: Armed Islamic Group

GMA: Mourabitounes Group of Azawad

GSL: Free Salafist Group

GSPC: Salafist Group for Call and Combat

Islamic Emirate of Barqa

Islamic State of Tripoli

Knights of Change

Libya Shield Brigade

LIDD: The Islamic League for Preaching and Holy Struggle

Martyrs’ Brigade

MUJAO: Movement for Unity and Jihad in West Africa

23

Muslim Brotherhood

Nawasi Brigade

Nusur al-Sahel Brigade

Rafallah Sehati Brigade

Soldiers of the Caliphate in Algeria

Those Who Signed in Blood

Timizart Brigade

24

Appendix 2. Aggression levels for all groups that have more than one enemy

Group aggression out aggression in aggression Rioters (Libya) 1.32 1.32 0.00 Military Forces of Libya 0.43 0.50 0.07 MUJAO 0.32 0.84 0.53 Military Forces of Algeria 0.28 0.50 0.21 Protesters (Mali) 0.21 0.21 0.00 Protesters (Libya) 0.19 0.19 0.00 GIA 0.14 0.31 0.17 Military Forces of Tunisia 0.14 0.14 0.00 Police Forces of Tunisia 0.13 0.13 0.00 Unidentified Armed Group (Algeria) 0.11 0.11 0.00 Civilians (France) 0.11 0.26 0.15 GMA 0.10 0.16 0.06 Libya Shield Brigade 0.09 0.54 0.45 Military Forces of Chad 0.09 0.12 0.04 Military Forces of Libya Special Forces 0.06 0.13 0.06 Libyan Rebel Forces 0.06 0.27 0.20 LIDD 0.06 0.09 0.03 GSPC 0.05 0.31 0.26 AQIM 0.05 0.76 0.71 Military Forces of Nigeria 0.04 0.09 0.05 Wershefana Communal Militia (Libya) 0.03 0.14 0.10 GLD 0.01 0.04 0.04 Boko Haram 0.01 0.19 0.18 Ansar Dine 0.00 0.42 0.42 El-Farouk Brigade 0.00 0.06 0.06 Military Forces of Mali 0.00 0.22 0.22 MNLA 0.00 0.23 0.23 Military Forces of France 0.00 0.25 0.25 Those Who Signed in Blood -0.01 0.09 0.09 Martyrs Brigade -0.02 0.04 0.06 February 17 Martyrs Brigade -0.02 0.16 0.18 Patriot Militia of Algerian Government -0.03 0.12 0.15 Abu Salim Martyrs Brigade -0.04 0.00 0.04 Civilians (Nigeria) -0.04 0.05 0.09 Military Forces of Mauritania -0.05 0.05 0.10 Military Forces of Niger -0.07 0.10 0.17 Al Qaqa Brigade -0.07 0.00 0.07 Ansaru -0.08 0.04 0.12

25

Police Forces of Algeria -0.08 0.13 0.21 FIS -0.08 0.00 0.08 Al Qaeda -0.10 0.21 0.31 Unidentified Armed Group (Libya) -0.10 0.37 0.48 Civilians (Libya) -0.12 0.09 0.21 Police Forces of Morocco -0.12 0.00 0.12 Civilians (Niger) -0.12 0.00 0.12 Civilians (Algeria) -0.12 0.08 0.21 Rafallah Sehati Brigade -0.13 0.00 0.13 UN -0.14 0.07 0.21 Zawia Ethnic Militia (Libya) -0.16 0.00 0.16 Civilians (Morocco) -0.16 0.00 0.16 Civilians (International) -0.20 0.04 0.24 Soldiers of the Caliphate in Algeria -0.21 0.00 0.21 Civilians (Mali) -0.36 0.00 0.36 Ansar al-Sharia -0.52 0.53 1.05 Muslim Brotherhood -0.91 0.00 0.91

Note: For each group, the out aggression is the average length of outgoing attack ties in the

embedded graph, in aggression is the average length of incoming attack ties, and net aggression

is the difference of the two.

26

Appendix 3. Aggression levels for Libyan organizations

Group aggression out aggression in aggression Protesters 1.24 1.24 0.00 Military Forces 0.77 0.83 0.07 Libyan Rebel Forces 0.41 0.68 0.28 Libya Shield Brigade 0.36 1.13 0.77 Wershefana Communal Militia 0.20 0.51 0.31 Misratah Communal Militia 0.00 0.32 0.32 Abu Salim Martyrs Brigade 0.00 0.06 0.06 Ansar al-Sharia -0.04 0.70 0.74 Islamist Militia -0.06 0.00 0.06 Brega Martyrs Brigade -0.06 0.00 0.06 Vigilante Militia -0.07 0.00 0.07 Al Qaeda -0.09 0.00 0.09 Al Qaqa Brigade -0.11 0.85 0.96 Zintan Ethnic Militia -0.22 0.00 0.22 Operation Libya Dawn -0.23 0.00 0.23 Zawia Ethnic Militia -0.25 0.00 0.25 Civilians -0.26 0.22 0.48 Gharyan Communal Militia -0.30 0.00 0.30 February 17 Martyrs Brigade -0.47 0.06 0.53 Rafallah Sehati Brigade -0.81 0.00 0.81

Source: ACLED. Calculations: authors. Note: the following organizations with entirely zero

rows have been removed from the table: El-Farouk Brigade, Al-Sawaiq Battalion, BSRC,

Journalists, Police Forces, Salafist Group, Mutiny of Military Forces, Janzur Communal Militia,

Awlad Suleiman Ethnic Militia, Shura Council of Benghazi Revolutionaries.

27

Appendix 4. Aggression levels for Nigerian organizations

Group aggression out aggression in aggression Boko Haram 1.08 3.51 2.43 Martyrs Brigade 0.98 0.98 0.00 Ansaru 0.72 1.09 0.36 Shuwa Ethnic Militia 0.48 0.48 0.00 Lassa Communal Militia 0.47 0.47 0.00 Kawuri Communal Militia 0.42 0.42 0.00 Military Forces 0.36 0.41 0.04 Attagara Communal Militia 0.32 0.32 0.00 Civilian Joint Task Force 0.04 0.04 0.00 Borno Vigilance Youths Group 0.04 0.04 0.00 Unidentified Armed Group 0.02 0.02 0.00 Civilians (Lebanon) 0.00 0.00 0.00 Police Forces 0.00 0.04 0.04 Vigilante Militia 0.00 0.04 0.04 Militia (Ali Kwara) 0.00 0.00 0.00 Fulani Ethnic Group 0.00 0.00 0.00 All Progressives Congress 0.00 0.00 0.00 VGN: Vigilante Group 0.00 0.48 0.48 Shiite Muslim Group 0.00 0.00 0.00 Civilians (China) -0.03 0.00 0.03 UN -0.04 0.00 0.04 Christian Militia -0.31 0.00 0.31 Civilians (International) -0.57 0.00 0.57 Military Forces Joint Task Force -0.64 0.00 0.64 Civilians (South Korea) -0.70 0.00 0.70 Private Security Forces -0.78 0.00 0.78 Civilians (Europe) -0.89 0.00 0.89 Civilians -0.98 0.04 1.02

Source: ACLED. Calculations: authors. Note: the following organizations with entirely zero

rows have been removed from the table: ANPP, Prison Guards, Muslim Group, Christian Group,

Students, PDP, Government, Military Forces UK, Igbo Ethnic Group.

1 MaliActu. 2016. “Mali: Iyad Ag Ghaly (Ancardine) Souhaiterait Un Cessez Le Feu,” last

accessed 30 October, http://maliactu.net/mali-iyad-ag-ghaly-ancardine-souhaiterait-un-

cessez-le-feu

28

2 Christia, Fotini, Alliance formation in civil wars. (Cambridge University Press, 2012). 3 Lacher, Wolfram. Organized crime and conflict in the Sahel-Sahara region. Vol. 1.

(Washington DC: Carnegie Endowment for International Peace, 2012); Bøås, Morten.

2015. The Politics of Conflict Economies: Miners, Merchants and Warriors in the

African Borderland. (London, Routledge). 4 Lecocq, Baz, Gregory Mann, Bruce Whitehouse, Dida Badi, Lotte Pelckmans, Nadia Belalimat,

Bruce Hall, and Wolfram Lacher, “One Hippopotamus and Eight Blind Analysts: A

Multivocal Analysis of the 2012 Political Crisis in the Divided Republic of Mali,”

Review of African Political Economy 40, no. 137 (2013): 343-357; Harmon, Stephen A.

Terror and insurgency in the Sahara-Sahel region: corruption, contraband, jihad and

the Mali war of 2012-2013 (Ashgate Publishing, Ltd., 2014); Wehrey, Frederic and

Boukhars, Anouar (eds) Perilous Desert. Insecurity in the Sahara (Carnegie

Endowment, 2013); Dowd, Caitriona “Fragmentation, conflict, and competition:

Islamist anti-civilian violence in sub-Saharan Africa”, Terrorism and Political Violence

(2016) DOI:10.1080/09546553.2016.1233870; Gow, James, Olonisakin, Funmi,

Dijxhoorn, Ernst (eds) Militancy and Violence in West Africa. (London, Routledge,

2013). 5 Walther, Olivier and Antonin Tisseron “Strange Bedfellows: A Network Analysis of Mali’s

Northern Conflict,” The Broker, (2015) Dec 18; Bencherif, Adib and Aurélie Campana.

“Alliances Of Convenience: Assessing The Dynamics Of The Malian Insurgency,”

Mediterranean Politics (2016): 1-20.http://dx.doi.org/10.1080/13629395.2016.1230942 6 Bakke, Kristin M., Kathleen Gallagher Cunningham, and Lee J.M. Seymour, “A Plague of

Initials: Fragmentation, Cohesion, And Infighting in Civil Wars,” Perspectives on

Politics 10, no. 02 (2012): 265-283; Cunningham, Kathleen Gallagher, Kristin M.

Bakke, and Lee JM Seymour. “Shirts Today, Skins Tomorrow Dual Contests And The

Effects Of Fragmentation In Self-Determination Disputes,” Journal of Conflict

Resolution 56, no. 1 (2012): 67-93. 7 Findley, Michael and Peter Rudloff, "Combatant Fragmentation and the Dynamics of Civil

Wars,” British Journal of Political Science 42, no. 04 (2012): 879-901. 8 Walther, Olivier J. and Dimitris Christopoulos, “Islamic Terrorism and The Malian Rebellion,”

Terrorism and Political Violence 27, no. 3 (2015): 497-519; Zheng, Quan, David B.

29

Skillicorn, and Olivier Walther, “Signed Directed Social Network Analysis Applied To

Group Conflict,” In 2015 IEEE International Conference on Data Mining Workshop

(ICDMW), pp. 1007-1014, DOI 10.1109/ICDMW.2015.107. 9 Hegre, Håvard, Gudrun Østby, and Clionadh Raleigh, "Poverty And Civil War Events A

Disaggregated Study Of Liberia," Journal of Conflict Resolution 53, no. 4 (2009): 598-

623; Cederman, Lars-Erik and Kristian Skrede Gleditsch, "Introduction To Special

Issue On" Disaggregating Civil War," Journal of Conflict Resolution (2009); Salehyan,

Idean. Rebels without borders. (Cornell University Press, 2009); Zammit-Mangion,

Andrew, Michael Dewar, Visakan Kadirkamanathan, Anaïd Flesken, and Guido

Sanguinetti. Modeling Conflict Dynamics With Spatio-Temporal Data (Springer

International Publishing, 2013); Dowd, Caitriona, "Cultural And Religious Demography

And Violent Islamist Groups In Africa," Political Geography 45 (2015a): 11-21;

Metternich, Nils W., Shahryar Minhas, and Michael D. Ward, "Firewall? or Wall on

Fire? A Unified Framework of Conflict Contagion and the Role of Ethnic Exclusion,"

Journal of Conflict Resolution (2015): 0022002715603452. 10 For a review see O’Loughlin, John and Clionadh Raleigh, “The Spatial Analysis Of Civil War

Violence,” in A Handbook of Political Geography, edited by Kevin Cox, Murray Low,

and Jennifer Robinson (Thousand Oaks, Sage, 2008), 493–508. 11 Cederman, Lars-Erik, Halvard Buhaug, and Jan Ketil Rød, "Ethno-Nationalist Dyads and Civil

War A GIS-Based Analysis," Journal of Conflict Resolution 53, no. 4 (2009): 496-525;

Metternich, Nils W., Shahryar Minhas, and Michael D. Ward, "Firewall? or Wall on

Fire? A Unified Framework of Conflict Contagion and the Role of Ethnic Exclusion,”

Journal of Conflict Resolution (2015): 0022002715603452; Phillips, Brian J. "Enemies

With Benefits? Violent Rivalry And Terrorist Group Longevity,” Journal of Peace

Research 52, no. 1 (2015): 62-75. 12 Kaldor, Mary. New And Old Wars: Organised Violence In A Global Era. (Stanford, Stanford

University Press, 2012). 13 Williams, Paul. War and Conflict in Africa. (Cambridge: Polity Press, 2016). 14 Weiss, Caleb. “Merger of al Qaeda groups threatens security in West Africa,” The Long War

Journal, 18 March, 2017. 15 Pearlman, Wendy and Kathleen Gallagher Cunningham, "Nonstate Actors, Fragmentation, And

Conflict Processes,” Journal of Conflict Resolution 56, no. 1 (2012): 3-15; Dowd,

30

Caitriona, "Actor Proliferation And The Fragmentation Of Violent Groups In Conflict,”

Research & Politics 2, no. 4 (2015b): 2053168015607891; Asal, Victor H., Hyun Hee

Park, R. Karl Rethemeyer, and Gary Ackerman, "With Friends Like These… Why

Terrorist Organizations Ally,” International Public Management Journal 19, no. 1

(2016): 1-30. 16 Staniland, Paul. Networks of rebellion: Explaining insurgent cohesion and collapse (Cornell

University Press, 2014). 17 Shapiro, Jacob N. The Terrorist's Dilemma: Managing violent covert organizations (Princeton

University Press, 2013). 18 Cunningham, Kathleen Gallagher, "Actor Fragmentation And Civil War Bargaining: How

Internal Divisions Generate Civil Conflict,” American Journal of Political Science 57,

no. 3 (2013): 659-672. 19 Cunningham, Kathleen Gallagher, "Divide And Conquer Or Divide And Concede: How Do

States Respond To Internally Divided Separatists?," American Political Science Review

105, no. 02 (2011): 275-297. 20 Bakke, Kristin M., Kathleen Gallagher Cunningham, and Lee J.M. Seymour. "A Plague Of

Initials: Fragmentation, Cohesion, And Infighting In Civil Wars,” Perspectives on

Politics 10, no. 02 (2012): 265-283; Cunningham, Kathleen Gallagher, Kristin M.

Bakke, and Lee JM Seymour. "Shirts Today, Skins Tomorrow Dual Contests And The

Effects Of Fragmentation In Self-Determination Disputes,” Journal of Conflict

Resolution 56, no. 1 (2012): 67-93. 21 Cunningham, David E. "Veto Players And Civil War Duration,” American Journal of Political

Science 50, no. 4 (2006): 875-892. 22 Findley, Michael and Peter Rudloff. "Combatant Fragmentation And The Dynamics Of Civil

Wars,” British Journal of Political Science 42, no. 04 (2012): 879-901. 23 Fjelde, Hanne and Desirée Nilsson. "Rebels Against Rebels Explaining Violence Between Rebel

Groups,” Journal of Conflict Resolution 56, no. 4 (2012): 604-628. 24 Nygård, Håvard Mokleiv and Michael Weintraub. "Bargaining Between Rebel Groups And

The Outside Option Of Violence,” Terrorism and Political Violence 27, no. 3 (2015):

557-580.

31

25 Bapat, Navin A. and Kanisha D. Bond. "Alliances Between Militant Groups,” British Journal

of Political Science 42, no. 4 (2012): 793-824. 26 Fjelde, Hanne and Desirée Nilsson. "Rebels against rebels explaining violence between rebel

groups,” Journal of Conflict Resolution 56, no. 4 (2012): 604-628. 27 Akcinaroglu, Seden. "Rebel interdependencies and civil war outcomes,” Journal of Conflict

Resolution 56, no. 5 (2012): 879-903. 28 Christia, Fotini. Alliance formation in civil wars. (Cambridge University Press, 2012). 29 Pearlman, Wendy and Kathleen Gallagher Cunningham. "Nonstate Actors, Fragmentation,

And Conflict Processes,” Journal of Conflict Resolution 56, no. 1 (2012): 3-15; Ingiriis,

Mohamed Haji. "African Conflicts and Informal Power: Big Men and Networks ed. by

Mats Utas (review),” Africa Today 60, no. 4 (2014): 92-93. 30Brass, Daniel J. and David M. Krackhardt. Power, politics, and social networks in

organizations, in Politics in Organizations: Theory and Research Consideration, edited

by Gerald R. Ferris, Treadway Darren C. (New York: Routledge, 2012), 355-375; Burt,

Ronald S. Structural holes: The social structure of competition. (Harvard University

Press, 2009). 31 Newman, Mark. Networks: an introduction. (Oxford University Press, 2010). 32 Maoz, Zeev, Ranan D. Kuperman, Lesley Terris, and Ilan Talmud. "Structural Equivalence

And International Conflict A Social Networks Analysis,” Journal of Conflict Resolution

50, no. 5 (2006): 664-689. 33 Flint, Colin, Paul Diehl, Jürgen Scheffran, John Vasquez, and Sang-hyun Chi.

"Conceptualizing Conflictspace: Toward A Geography Of Relational Power And

Embeddedness In The Analysis Of Interstate Conflict,” Annals of the Association of

American Geographers 99, no. 5 (2009): 827-835; Radil, Steven M. and Colin Flint.

"Exiles and arms: the territorial practices of state making and war diffusion in post–

Cold War Africa,” Territory, Politics, Governance 1, no. 2 (2013): 183-202. 34 Everett, Martin G. and Stephen P. Borgatti. "Networks Containing Negative Ties,” Social

Networks 38 (2014): 111-120. 35 Huitsing, Gijs, Marijtje AJ Van Duijn, Tom AB Snijders, Peng Wang, Miia Sainio, Christina

Salmivalli, and René Veenstra. "Univariate And Multivariate Models Of Positive And

32

Negative Networks: Liking, Disliking, And Bully–Victim Relationships,” Social

Networks 34, no. 4 (2012): 645-657. 36 Everett, Martin G. and Stephen P. Borgatti. "Networks Containing Negative Ties,” Social

Networks 38 (2014): 111-120. 37 Labianca, Giuseppe and Daniel J. Brass. "Exploring The Social Ledger: Negative

Relationships And Negative Asymmetry In Social Networks In Organizations,”

Academy of Management Review 31, no. 3 (2006): 596-614; Grosser, Travis J., Virginie

Lopez-Kidwell, and Giuseppe Labianca. "A Social Network Analysis Of Positive And

Negative Gossip In Organizational Life,” Group & Organization Management 35, no. 2

(2010): 177-212; Rambaran, J. Ashwin, Jan Kornelis Dijkstra, Anke Munniksma, and

Antonius HN Cillessen. "The development of adolescents’ friendships and antipathies:

A longitudinal multivariate network test of balance theory,” Social Networks 43 (2015):

162-176. 38 Doreian, Patrick and Andrej Mrvar. "Structural Balance And Signed International Relations,”

Journal of Social Structure 16 (2015): 1. 39 Smith, Jason M., Daniel S. Halgin, Virginie Kidwell-Lopez, Giuseppe Labianca, Daniel J.

Brass, and Stephen P. Borgatti. "Power In Politically Charged Networks,” Social

Networks 36 (2014): 162-176. 40 Raleigh, Clionadh and Caitriona Dowd. "Armed Conflict Location And Event Data Project

(ACLED) Codebook,” (2015): 24.

content/uploads/2015/01/ACLED_Codebook_2015.pdf 41 Algeria, Benin, Burkina Faso, Cameroon, Chad, Gambia, Ghana, Guinea, Guinea Bissau,

Ivory Coast, Liberia, Mauritania, Morocco, Libya, Niger, Nigeria, Mali, Sierra Leone,

Senegal, Tunisia and Togo. 42 Freeman, Linton C. "Centrality In Social Networks Conceptual Clarification,” Social networks

1, no. 3 (1979): 215-239. 43 Zheng, Quan and David B. Skillicorn. "Spectral Embedding Of Signed Networks,” In SIAM

International Conference on Data Mining, pp. 55-63. 2015., DOI

10.1137/1.9781611974010.7; Zheng, Quan, David B. Skillicorn, and Olivier Walther.

"Signed Directed Social Network Analysis Applied To Group Conflict,” In 2015 IEEE

33

International Conference on Data Mining Workshop (ICDMW), pp. 1007-1014. IEEE,

2015. , DOI 10.1109/ICDMW.2015.107. 44 Huitsing, Gijs, Marijtje AJ Van Duijn, Tom AB Snijders, Peng Wang, Miia Sainio, Christina

Salmivalli, and René Veenstra. "Univariate And Multivariate Models Of Positive And

Negative Networks: Liking, Disliking, And Bully–Victim Relationships,” Social

Networks 34, no. 4 (2012): 645-657. 45 Radil, Steven. “Toward a network theory of the diffusion of ‘new wars’”, Paper presented at

the DASTI workshop on transnational extremist organizations, Rutgers University, 19-

20 September 2016. 46 Williams, Paul. War and Conflict in Africa. (Cambridge: Polity Press, 2016). 47 Labianca, Giuseppe and Daniel J. Brass. "Exploring The Social Ledger: Negative

Relationships And Negative Asymmetry In Social Networks In Organizations,”

Academy of Management Review 31, no. 3 (2006): 596-614. 48 Smith, Jason M., Daniel S. Halgin, Virginie Kidwell-Lopez, Giuseppe Labianca, Daniel J.

Brass, and Stephen P. Borgatti. "Power In Politically Charged Networks,” Social

Networks 36 (2014): 162-176. 49 Dakono, Baba. 2013. “Who’s Who In Northern Mali?” ISS, Institute for Security Studies,

https://www.issafrica.org/iss-today/whos-who-in-northern-mali 50 Details of the mathematical constructions can be found in Zheng, Quan and Skillicorn, David B. Social Networks with Rich Edge Semantics. (Taylor and Francis, 2017).