Question: What was the faction called that supported the Pope and the Holy Roman Emperor in the Italian city-states and that Alberico da Romano was a statesman of in the 1100's?

Context paragraphs:
Concordat of Worms: The Concordat of Worms (Latin: "Concordatum Wormatiense" ), sometimes called the Pactum Calixtinum by papal historians, was an agreement between Pope Calixtus II and Holy Roman Emperor Henry V on September 23, 1122, near the city of Worms.  It brought to an end the first phase of the power struggle between the Papacy and the Holy Roman Emperors and has been interpreted as containing within itself the germ of nation-based sovereignty that would one day be confirmed in the Treaty of Westphalia (1648).  In part this was an unforeseen result of strategic maneuvering between the Church and the European sovereigns over political control within their domains.  The King was recognised as having the right to invest bishops with secular authority ("by the lance") in the territories they governed, but not with sacred authority ("by ring and staff").  The result was that bishops owed allegiance in worldly matters both to the pope and to the king, for they were obliged to affirm the right of the sovereign to call upon them for military support, under his oath of fealty.  Previous Holy Roman Emperors had thought it their right, granted by God, to name Church officials within their territories (such as bishops) and to confirm the Papal election (and, at times of extraordinary urgency, actually name popes).  In fact, the Emperors had been heavily relying on bishops for their secular administration, as they were not hereditary or quasi-hereditary nobility with family interests.  A more immediate result of the Investiture struggle identified a proprietary right that adhered to sovereign territory, recognising the right of kings to income from the territory of a vacant diocese and a basis for justifiable taxation.  These rights lay outside feudalism, which defined authority in a hierarchy of personal relations, with only a loose relation to territory.  The pope emerged as a figure above and out of the direct control of the Holy Roman Emperor.

Italian cruiser Alberico da Barbiano: Alberico da Barbiano was an Italian "Giussano"-class light cruiser, that served in the Regia Marina during World War II.  She was named after Alberico da Barbiano, an Italian condottiero of the 14th century.

List of Holy Roman Empresses: Holy Roman Empress or Empress of the Holy Roman Empire is the title given to the consort (wife) or regent of the Holy Roman Emperor.  The elective dignity of Holy Roman Emperor was restricted to males only, therefore there was never a Holy Roman Empress regnant, though women such as Theophanu or Maria Theresa of Austria, who controlled the power of rule, served as de facto Empresses regnant.

Alberico da Barbiano: Alberico da Barbiano (c. 1344–1409) was the first of the Italian condottieri.  His master in military matters was the English mercenary John Hawkwood, known in Italy as Giovanni Acuto.  Alberico's "compagnia" fought under the banner of Saint George, as the "compagnia San Giorgio".

Guelphs and Ghibellines: The Guelphs and Ghibellines ( ; , also , ; Italian: "guelfi e ghibellini" ] ) were factions supporting the Pope and the Holy Roman Emperor, respectively, in the Italian city-states of central and northern Italy.  During the 12th and 13th centuries, rivalry between these two parties formed a particularly important aspect of the internal politics of medieval Italy.  The struggle for power between the Papacy and the Holy Roman Empire had arisen with the Investiture Controversy, which began in 1075 and ended with the Concordat of Worms in 1122.  The division between the Guelphs and Ghibellines in Italy, however, persisted until the 15th century.

Cunizza da Romano: Cunizza da Romano (born c. 1198) was an Italian noblewoman, the third daughter of Ezzelino II da Romano and Adelaide di Mangona, and sister to Ezzelino III and Alberico da Romano.

Alberico da Romano: Alberico da Romano (1196 – 26 August 1260), called Alberico II, was an Italian condottiero, troubadour, and an alternatingly Guelph and Ghibelline statesman.  He was also a patron of Occitan literature.

Papal election, 1241: The papal election, following the death of Pope Gregory IX, from September 21 to October 25, 1241 elected Cardinal Goffredo da Castiglione as Pope Celestine IV.  The election took place during the first of many protracted "sede vacantes" of the Middle Ages, and like many of them was characterized by disputes between popes and the Holy Roman Emperor.  Specifically, the election took place during the war between Frederick II, Holy Roman Emperor against the Lombard League and the deceased pontiff, Pope Gregory IX, with Italy divided between pro-Papal and pro-Imperial factions known as the Guelphs and Ghibellines.

Antipope Clement III: Guibert or Wibert of Ravenna ( 1029 – 8 September 1100) was an Italian prelate, archbishop of Ravenna, who was elected pope in 1080 in opposition to Pope Gregory VII.  Gregory was the leader of the movement in the church which opposed the traditional claim of European monarchs to control ecclesiastical appointments, and this was opposed by supporters of monarchical rights led by the Holy Roman Emperor.  This led to the conflict known as the Investiture Controversy.  Gregory was felt by many to have gone too far when he excommunicated the Holy Roman Emperor Henry IV and supported a rival claimant as emperor, and in 1080 the pro-imperial Synod of Brixen pronounced that Gregory was deposed and replaced as pope by Guibert.

Treaty of Venice: The Treaty or Peace of Venice, 1177, was a peace treaty between the papacy and its allies, the north Italian city-states of the Lombard League, and Frederick I, Holy Roman Emperor.  The Norman Kingdom of Sicily also took part in negotiations and the treaty thereby determined the political course of all Italy for the next several years.

Supporting paragraphs: Alberico da Romano Guelphs and Ghibellines
Answer: The Guelphs and Ghibellines