The Church was hierarchical in nature
“And thus preaching through countries and cities, they appointed the first-fruits [of their labours], having first proved them by the Spirit, to be bishops and deacons of those who should afterwards believe. Nor was this any new thing, since indeed many ages before it was written concerning bishops and deacons. For thus saith the Scripture a certain place, ‘I will appoint their bishops s in righteousness, and their deacons in faith.’… Our apostles also knew, through our Lord Jesus Christ, and there would be strife on account of the office of the episcopate. For this reason, therefore, inasmuch as they had obtained a perfect fore-knowledge of this, they appointed those [ministers] already mentioned, and afterwards gave instructions, that when these should fall asleep, other approved men should succeed them in their ministry…For our sin will not be small, if we eject from the episcopate those who have blamelessly and holily fulfilled its duties.” Pope Clement, Epistle to Corinthians, 42, 44 (A.D. 98).
“Since therefore I have, in the persons before mentioned, beheld the whole multitude of you in faith and love, I exhort you to study to do all things with a divine harmony, while your bishop presides in the place of God, and your presbyters in the place of the assembly of the apostles, along with your deacons, who are most dear to me, and are entrusted with the ministry of Jesus Christ, who was with the Father before the beginning of time, and in the end was revealed…Let nothing exist among you that may divide you ; but be ye united with your bishop, and those that preside over you, as a type and evidence of your immortality.” Ignatius of Antioch, Epistle to the Magnesians, 6 (c. A.D. 110).
“For what is the bishop but one who beyond all others possesses all power and authority, so far as it is possible for a man to possess it, who according to his ability has been made an imitator of the Christ off God? And what is the presbytery but a sacred assembly, the counselors and assessors of the bishop? And what are the deacons but imitators of the angelic powers, fulfilling a pure and blameless ministry unto him, as…Anencletus and Clement to Peter?” Ignatius, To the Trallians, 7 (A.D. 110)
“See that ye all follow the bishop, even as Jesus Christ does the Father, and the presbytery as ye would the apostles; and reverence the deacons, as being the institution of God. Let no man do anything connected with the Church without the bishop. Let that be deemed a proper Eucharist, which is [administered] either by the bishop, or by one to whom he has entrusted it. Wherever the bishop shall appear, there let the multitude [of the people] also be; even as, wherever Jesus Christ is, there is the Catholic Church. It is not lawful without the bishop either to baptize or to celebrate a love-feast; but whatsoever he shall approve of, that is also pleasing to God, so that everything that is done may be secure and valid.” Ignatius of Antioch, Epistle to the Smyraens, 8 (c. A.D. 110).
“Hegesippus and the Events which he mentiones. Hegesippus in the five books of Memoirs which have come down to us has left a most complete record of his own views. In them he states that on a journey to Rome he met a great many bishops, and that he received the same doctrine from all. It is fitting to hear what he says after making some remarks about the epistle of Clement to the Corinthians. His words are as follows: And the church of Corinth continued in the true faith until Primus was bishop in Corinth. I conversed with them on my way to Rome, and abode with the Corinthians many days, during which we were mutually refreshed in the true doctrine. And when I had come to Rome I remained a there until Anicetus, whose deacon was Eleutherus. And Anicetus was succeeded by Soter, and he by Eleutherus. In every succession, and in every city that is held which is preached by the law and the prophets and the Lord.’” Hegesippus, fragment in Eusebius Ecclesiastical History, 4:22 (c. A.D. 180).